diff --git a/content/notebooks/MLE.ipynb b/content/notebooks/MLE.ipynb
index 26382ed8..e3b70d9e 100644
--- a/content/notebooks/MLE.ipynb
+++ b/content/notebooks/MLE.ipynb
@@ -2,8 +2,13 @@
  "cells": [
   {
    "cell_type": "code",
-   "execution_count": 11,
+   "execution_count": null,
+   "id": "0008855f-8f43-432c-a9aa-1b9e50237421",
    "metadata": {
+    "editable": true,
+    "slideshow": {
+     "slide_type": ""
+    },
     "tags": [
      "remove-cell"
     ]
@@ -15,6 +20,7 @@
   },
   {
    "cell_type": "markdown",
+   "id": "fabdc43f-85b0-4c6b-99c9-71ec09f88263",
    "metadata": {},
    "source": [
     "# Model Fitting using Maximum Likelihood"
@@ -22,142 +28,333 @@
   },
   {
    "cell_type": "markdown",
-   "metadata": {},
+   "id": "5f6b676e-ead2-4180-a9bf-8a2387a19622",
+   "metadata": {
+    "editable": true,
+    "slideshow": {
+     "slide_type": ""
+    },
+    "tags": []
+   },
    "source": [
     "## Introduction\n",
     "\n",
-    "\n",
-    "In this Chapter we will work through various examples of  model fitting  to biological data using Maximum Likelihood. It is recommended that you see the [lecture](https://github.com/mhasoba/TheMulQuaBio/tree/master/content/lectures/ModelFitting) on model fitting in Ecology and Evolution. \n",
+    "In this Chapter we learn about and work through various examples of model fitting to biological data using Maximum Likelihood. It is recommended that you see this introductory [lecture](https://github.com/MulQuaBio/MQB/tree/main/content/lectures/EnE_Modelling_Intro) on model fitting in Ecology and Evolution. \n",
     "\n",
     "[Previously](./NLLS.ipynb), we learned how to fit a mathematical model/equation to data by using the Least Squares method (linear or nonlinear). That is, we choose the parameters of model being fitted (e.g., straight line) to minimize the sum of the squares of the residuals/errors around the fitted model. \n",
     "\n",
-    "An alternative to minimizing the sum of squared errors is to find parameters to the function such that the * likelihood * of the parameters, given the data and the model, is maximized. Please see the [lectures](https://github.com/vectorbite/VBiTraining2/tree/master/lectures) for the theoretical background to the following examples.\n",
+    "An alternative to minimizing the sum of squared errors is to find parameters to the function such that the * likelihood * of the parameters, given the data and the model, is maximized. \n",
+    "\n",
+    "<!-- Please see the [lectures](https://github.com/vectorbite/VBiTraining2/tree/master/lectures) for the theoretical background to the following examples.\n",
+    " -->"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "0182cf96-7230-47aa-9173-5fe7ba63b2d9",
+   "metadata": {
+    "editable": true,
+    "jp-MarkdownHeadingCollapsed": true,
+    "slideshow": {
+     "slide_type": ""
+    },
+    "tags": []
+   },
+   "source": [
+    "## Probability review\n",
+    "\n",
+    "We will begin with a review of foundational probability theory.\n",
+    "<!-- \n",
+    "Axioms. Common discrete and continuous random variables, probability mass and density functions, cumulative functions.\n",
+    "\n",
+    "Expectation, variance, statistical moments, moment generating functions. \n",
+    "\n",
+    "Central limit theorem, Weak law of large numbers. \n",
+    " -->\n",
+    "\n",
+    "<!-- #### Acknowledgements\n",
+    "This series of five notebooks are compiled by Tin-Yu Hui based on existing materials. Special thanks to Dan Reuman who used to teach this module a long time ago. Some examples are extracted from Mick Crawley's GLM course, where I had the pleasure to attend, both as a student and as a GTA. Any errors that remain are, of course, my sole responsibility. \n",
+    " -->\n",
+    "\n",
+    "### The three axioms of probability\n",
+    "\n",
+    "These axioms are the building blocks of modern theories of probability and statistics. \n",
+    "\n",
+    "1) For any event $A$ in a sample space $S$, $Pr(A)\\geqslant 0$.\n",
+    "\n",
+    "2) $Pr(S)=1$\n",
+    "   \n",
+    "3) For disjoint events $A_1, A_2, A_3, ...$, then $Pr(A_1\\cup A_2\\cup A_3\\cup ...)=Pr(A_1)+Pr(A_2)+Pr(A_3)+...$\n",
+    "\n",
+    "We assign a probability measure $Pr(A)$ to an event $A$. The first axiom states that probability is always non-negative. The smallest probability is zero (i.e. impossible). The second axiom states that the probability of the whole sample space is one. The sample space $S$ contains all possible outcomes for the given random experiment. This also specifies the upper bound for a probability. For the third axiom, the probability of the union of disjoint (i.e. non-overlapping) events equals the sum of their individual probabilities. Think of a Venn diagram. \n",
+    "\n",
+    "### Random variables\n",
+    "A random variable (r.v.) is a variable that takes on its value by chance. A r.v. can take on a set of possible values, each with an associated probability. To fully characterise a r.v. we need to know 1) all its possible outcomes, which form the domain or support of the r.v., and 2) the probability of getting each outcome. \n",
+    "\n",
+    "Example: Let $X$ be the outcome of a coin toss. Certainly, $X$ is random. There can only be two possible outcomes: head or tail. If the coin is fair, then $Pr(X=head)=Pr(X=tail)=0.5$. These statements jointly characterise the r.v. $X$. \n",
+    "\n",
+    "#### Discrete random variables\n",
+    "Some r.v. take a discrete collection of values. We call them discrete r.v.. An example of a discrete r.v. is the outcome from rolling a fair die. \n",
     "\n",
-    "We will first implement the (negative log) likelihood for [simple linear regression (SLR)](./Regress.ipynb) in R. Recall that SLR assumes every observation in the dataset was generated by the model:\n",
+    "A probability *mass* function (pmf) for a discrete r.v. $X$ is a function that describes the relative probability that $X$ takes each of its possible values. In most textbooks, the pmf is written as $f(x)$ or $f_X(x)$. See #2. for more notations. \n",
+    "\n",
+    "##### Bernoulli random variable\n",
+    "A Bernoulli r.v. is the simplest r.v. with two outcomes: success (1) or failure (0). It has one parameter $p$, the probability of success, which is bounded between 0 and 1. If $X\\sim Bernoulli(p)$ then it is obvious that $Pr(X=1)=p$ and $Pr(X=0)=1-p$. While these two equations technically summarise the probabilities, the pmf has an alternative expression: $f_X(x)=p^x(1-p)^{1-x}$. \n",
+    "\n",
+    "Note that $f_X(x)=0$ elsewhere (outside of the support), but this statement is often too trivial to be included. \n",
+    "\n",
+    "##### Binomial random variable\n",
+    "A binomial r.v. is the sum of $n$ independent and identically distributed (i.i.d.) Bernoulli r.v. hence it takes values on $\\{0, 1, 2, ..., n\\}$. It is a two-parameter r.v.: $p$ the probability of success, inherited from Bernoulli r.v., and $n$ the number of i.i.d. Bernoulli trials. If $X\\sim binomial(n, p)$ then its pmf is$$\n",
+    " f_X(x)=C^n_{x}p^x(1-p)^{n-x}\n",
+    "$$ \n",
+    "\n",
+    "where $C^n_{x}$ is the number of combinations when we choose $x$ objects from $n$. Order of selection does not matter here. \n",
+    "\n",
+    "##### Poisson random variable\n",
+    "A Poisson r.v. models the number of events occurring in a fixed interval of time. Since it is a count, its possible values are all non-negative integers $\\{0, 1, 2, 3, ...\\}$. While there are infinitely many possible outcomes, it is still regarded as a discrete r.v.. \n",
+    "\n",
+    "Poisson has one parameter which is the rate of occurrance $\\lambda>0$. If $X\\sim Poisson(\\lambda)$ then$$\n",
+    " f_X(x)=\\frac{\\lambda^{x}e^{-\\lambda}}{x!}$$ \n",
+    "If $X\\sim binomial(n, p)$ with reasonably large $p$ and reasonably small $np$, then $X$ can be approximated by a Poisson r.v. with $\\lambda=np$. That is, the number of rare events can be modelled by Poisson. \n",
+    "\n",
+    "####  Continuous random variables\n",
+    "Continuous r.v., in contrast, take a whole range of real-number values (think of tomorrow's temperature or allele frequencies). To accommodate continuous r.v.., a probability *density* function (pdf) is in place to describe the relative probability that the r.v. takes each value in the range of possible values. \n",
+    "\n",
+    "Recall: The range of possible values within non-zero probability is called the *support* of a r.v.. \n",
+    "\n",
+    "#####  Uniform random variable\n",
+    "A uniform r.v. is a continous r.v. with two parameters $a$ and $b$, which are the lower and upper bounds (support). If $X\\sim U(a,b)$ then\n",
     "\n",
     "$$\n",
-    "Y_i = \\beta_0 + \\beta_1 X_i + \\varepsilon_i, \\;\\;\\; \\varepsilon_i \\stackrel{\\mathrm{iid}}{\\sim} \\mathrm{N}(0, \\sigma^2)\n",
+    "    f_X(x)=1/(b-a)\n",
     "$$\n",
     "\n",
-    "That is, this is a model for the * conditional distribution * of $Y$ given $X$. The pdf for the normal distribution is given by\n",
+    "which looks like a horizontal line from $a$ to $b$. \n",
     "\n",
+    "##### Exponential random variable\n",
+    "Exponential r.v. models the time between two successive events (remember Poisson r.v.?). Since it is a measure of time, it is continous with support $[0, \\infty)$ (inclusive of 0, but always smaller than infinity). A one-parameter r.v. which shares the same rate paramter $\\lambda$ with Poisson. If $X\\sim Exponential(\\lambda)$ then\n",
     "$$\n",
-    "f(x) = \\frac{1}{\\sqrt{2\\sigma^2 \\pi}} \\exp\\left(-\\frac{(x-\\mu)^2}{2\\sigma^2} \\right)\n",
+    " f_X(x)=\\lambda e^{-\\lambda x}$$ \n",
+    " \n",
+    "#####  Normal random variable\n",
+    "\n",
+    "Later, we will learn why normal is the most famous r.v. of all and why normal approximation usually holds even if we have limited knowledge of the underlying distribution. $X\\sim N(\\mu, \\sigma^2)$, it takes values over the entire real number line, from negative to positive infinity, or $x \\in \\Re$. Although its bell-shaped pdf is widely known and aesthetically pleasing, its mathematical form is not as memorable: \n",
+    "\n",
     "$$\n",
+    " f_X(x)=\\frac{1}{\\sqrt{2\\pi \\sigma}}e^{-\\frac{(x-\\mu)^2}{2\\sigma^2}}\n",
+    "$$ \n",
+    " \n",
+    "It is a two-parameter r.v. with $\\mu$ and $\\sigma^2$, if you have not already realised. \n",
+    "\n",
+    "####  Some notations\n",
+    "Most textbooks use the function $f()$ to denote a pmf/pdf. Some may specify the r.v. of interest through the subscript, e.g. $f_X()$. Capital letters are understood to be used for r.v. . The use of subscripts is extremely helpful when multiple r.v. are involved, say, when mentioning $X$ and $Y$ and their associated $f_X(x)$ and $f_Y(y)$. The lowercase $x$ inside the round brackets indicates the value at which the pmf/pdf is evaluated. These small $x$ or $y$ are real numbers (not r.v.). Numbers are numbers, r.v. are r.v.. \n",
     "\n",
-    "In the SLR model, the conditional distribution has * this * distribution. \n",
+    "Some texts may even state the associated parameter(s) $\\theta$ in the pmf/pdf, say, $f(x; \\theta)$ or $f(x|\\theta)$. The latter reads as \"$x$ given $\\theta$\". \n",
+    "\n",
+    "####  Built-in statistical tables in R\n",
+    "We should always make good use of the built-in statistical functions in R. For example, there are `pnorm()`, `dnorm`, `qnorm()`, and `rnorm()` for normal distribution. The prefix `p` returns the cmf/cdf (see #3.2 below), `d` for the pmf/pdf, `q` for quantiles (for hypothesis testing), and `r` for random number generation. We will experiment some of these functions in today's practical. \n",
+    "\n",
+    "### Probability and cumulative functions\n",
+    "\n",
+    "####  Properties of probability mass and density functions\n",
+    "\n",
+    "Per discussed, pmf/pdf are functions to describe the relative probabilities of the outcomes and to characterise a r.v.. From the first axiom, probabilities are non-negative, hence the pmf/pdf never go below the horizontal axis. From the second axiom, we learnt that the sum of pmf bars must be one:\n",
     "\n",
-    "That is, for any single observation, $y_i$\n",
     "$$\n",
-    "f(y_i|\\beta_0, \\beta_1, x_i) = \\frac{1}{\\sqrt{2\\sigma^2 \\pi}} \\exp\\left(-\\frac{(y_i-(\\beta_0+\\beta_1 x_i))^2}{2\\sigma^2} \\right)\n",
+    " \\sum_{all~possible~outcomes} f_X(x)=1\n",
+    "$$ \n",
+    " \n",
+    " For continuous case, if we take the limit of summation (of vertical bars) it becomes integration: \n",
+    "\n",
     "$$\n",
+    " \\int_{all~possible~outcomes} f_X(x)dx=1\n",
+    "$$ \n",
     "\n",
-    "Interpreting this function as a function of the parameters $\\theta=\\{ \\beta_0, \\beta_1, \\sigma \\}$, then it gives us the likelihood of the $i^{\\mathrm{th}}$ data point. \n",
+    "That is, the *area* under a pdf must be one. \n",
     "\n",
-    "As we did for the simple binomial distribution (see [lecture](https://github.com/vectorbite/VBiTraining2/tree/master/lectures)), we can use this to estimate the parameters of the model."
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "We will use R. For starters, clear all variables and graphic devices and load necessary packages:"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 12,
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "rm(list = ls())\n",
-    "graphics.off()"
+    "####  Cumulative mass and density functions\n",
+    "We use capital $F()$ for cumulative functions (cmf/cdf). As its name suggests, $F_X(x)=Pr(X\\leqslant x)$ by definition. It is a non-decreasing function with $F(-\\infty)=0$ and $F(\\infty)=1$. For discrete r.v., \n",
+    "$$\n",
+    " F_X(x)=\\sum_{x_i\\leqslant x}f_X(x_i)$$ For continuous case, $F_X(x)$ is the area under the pdf curve, from $-\\infty$ to $x$: \n",
+    "$$\n",
+    " F_X(x)=\\int_{-\\infty}^{x}f_X(t)dt$$ I hope you still remember the fundamental theorem of calculus. Conversely, we can obtain pdf by differentiating cdf. You only need either the cumulative or probability function to characterise a r.v. \n",
+    "\n",
+    "### Statistical moments and expectation\n",
+    "####  Expectation\n",
+    "Imagine an experiment that can be repeated for *infinitely* many times. Imagine you keep tossing a coin or keep drawing random numbers from a given distribution for *infinitely* many times. The expecation is the \"average\" of the said experiment. \n",
+    "\n",
+    "Of course, this \"average\" is hypthetical one as nobody can afford having *infinitely* many repeats. Here we describe the \"average\" behaviour of a r.v. on the population level. Try not to confuse with the \"sample average\" that we tend to calculate from real data. In fact, today's discussion does not involve any data. We are merely discussing the characteristics of r.v. based on some given random mechanisms. \n",
+    "\n",
+    "For discrete r.v., \n",
+    "$$\n",
+    " E[X]=\\sum_{all~possible~outcomes}xf(x)$$ For continuous r.v., \n",
+    "$$\n",
+    " E[X]=\\int_{-\\infty}^{+\\infty}xf(x)dx$$ You can replace the bounds of the integral by the support of $X$. $E[X]$ is the expected value of $X$, the \"average\" value weighted according to the pmf/pdf. $E[X]$ is also called the population mean or true mean of the r.v. $X$. It is a measure of central tendency. \n",
+    "\n",
+    "####  Variance\n",
+    "Similarly, we have the population variance, which is given by\n",
+    "$$\n",
+    " Var[X]=E[(X-E[X])^2]$$ The formula above suggests that variance is the expected distance squared of the r.v. $X$ from its population mean. In practice we tend to use this alternative form: \n",
+    "$$\n",
+    " Var[X]=E[X^2]-(E[X])^2$$ There is no surprise that variance is a measure of dispersion. \n",
+    "\n",
+    "####  Higher moments\n",
+    "In general, the $n^{th}$ *raw* moment of $X$ is $E[X^n]$: \n",
+    "$$\n",
+    " E[X^n]=\\int x^nf(x)dx$$ \n",
+    "And the $n^{th}$ central moment is $E[(X-E[X])^n]$. In most cases only the first few moments are studied. For example, the third moment of a r.v. describes its skewness (e.g., a normal r.v. has 0 skewness as a bell curve is symmetric about $\\mu$), and the fourth moments is a measure of kurtosis (fat tails). \n",
+    "\n",
+    "Note that not all distributions have finite moments. One example is the Cauchy distribution (t-distribution with 1 degree of freedom) whose $E[X]$ is undefined. \n",
+    "\n",
+    "####  More on the expectation operator\n",
+    "We get a real number after taking the expectation from a r.v., we get a real number. Note that expectation is linear: \n",
+    "$$\n",
+    " E[aX+bY]=aE[X]+bE[Y]$$ for any r.v. $X$, $Y$ and any real numbers $a$, $b$. \n",
+    "\n",
+    "In some cases, we may be required to transform a r.v. or to calculate the expectation of a transformed r.v.: \n",
+    "$$\n",
+    " E[g(X)]=\\int g(x)f(x)dx$$\n",
+    "  for any real function $g$. \n",
+    "\n",
+    "Note that $g(X)$ itself is another r.v. with its own support, pdf/pmf, expecation, etc.. The same is true for $(X+Y)$, that is, the sum (or prodictof r.v. is another r.v.. Remember, transformation of a r.v. yields another r.v.. A r.v. will not suddenly turn into a real number. \n",
+    "\n",
+    "####  Moment generating function\n",
+    "A moment-generating function (mgf) is the third way to characterise an r.v.. $M_X(t)$ is a carefully crafted function from $X$ such that it \"generates\" statistical moments through its derivatives at $t=0$, note that $t$ is a dummy variable. The $n^th$ moment of $X$ is: \n",
+    "$$\n",
+    " E[X^n]=\\frac{d^nM_X(t)}{dt^n}|_{t=0}$$\n",
+    "\n",
+    "For keen readers, $M_X(t)=E[e^{tX}]$. \n",
+    "\n",
+    "### Central limit theorem and Weak law of large numbers\n",
+    "####  Central limit theorem\n",
+    "Let $\\{X_1, X_2, X_3, ..., X_n\\}$ be i.i.d. r.v. with finite $E[X_i]=\\mu$ and finite $Var[X_i]=\\sigma^2$. Also let $\\bar{X_n}=(X_1+X_2+...+X_n)/n$ be the sample mean of these r.v. ($\\bar{X_n}$ is another r.v.). The central limit theorem states that as $n\\rightarrow \\infty$, the r.v. $\\sqrt{n}(\\bar{X_n}-\\mu)$ converges *in distribution* to a normal distribution: \n",
+    "$$\n",
+    " \\sqrt{n}(\\bar{X_n}-\\mu) \\xrightarrow{d} N(0,\\sigma^2)\n",
+    " $$ \n",
+    "\n",
+    "See today's practical for visualisation. \n",
+    "\n",
+    "####  Weak law of large numbers\n",
+    "\n",
+    "Let us consider a similar series of i.i.d. r.v. $\\{X_1, X_2, X_3, ..., X_n\\}$ with finite $E[X_i]=\\mu$. The weak law of large numbers states that the sample mean $\\bar{X_n}$ converges *in probability* to the expected value when $n\\rightarrow \\infty$. That is, for any postive $\\epsilon$, \n",
+    "\n",
+    "$$\n",
+    " \\lim_{n\\rightarrow \\infty}Pr(|\\bar{X_n}-\\mu|<\\epsilon)=1\n",
+    "$$"
    ]
   },
   {
    "cell_type": "markdown",
-   "metadata": {},
+   "id": "35372dfd-d19b-47ac-9548-f37525bfc213",
+   "metadata": {
+    "editable": true,
+    "slideshow": {
+     "slide_type": ""
+    },
+    "tags": []
+   },
    "source": [
-    "## Implementing the Likelihood in R\n",
     "\n",
-    "First, we need to build an R function that returns the (negative log) likelihood for simple linear regression (it is negative log because the log of likelihood is itself negative):"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 1,
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "nll.slr <- function(par, dat, ...){\n",
-    " args <- list(...)\n",
-    " \n",
-    " b0 <- par[1]\n",
-    " b1 <- par[2]\n",
-    " X <- dat$X\n",
-    " Y <- dat$Y\n",
-    " if(!is.na(args$sigma)){\n",
-    "  sigma <- args$sigma\n",
-    " } else \n",
-    "  sigma <- par[3]\n",
-    "\n",
-    " mu <- b0+b1 * X\n",
+    "## Multivariate random variables, Likelihood functions\n",
+    "\n",
+    "<!-- We will now learn about likelihood and log-likelihood functions, Point estimation, maximisation by hand, maximisation by computer, MLE coin-tossing example, i.i.d. normal example. \n",
+    " -->\n",
+    "\n",
+    "### Multivariate random variables\n",
+    "Quite often multiple r.v. are considered simultaneously in a system due to their interaction. For example, population sizes of the species within a predator-prey system, allele frequencies among tightly linked loci, traits within an individual, and many more. It is essential for us to extend the discussions of r.v. and pmf/pdf to multivariate cases. \n",
+    "\n",
+    "#### Joint probability density functions\n",
+    "Given a pair of r.v. $X$ and $Y$, the joint pmf/pdf is $f_{X,Y}(x,y)$, a higher-dimensional function. In this bivariate case the joint pdf can be visualised in the form of a 3D plot. Following the same rules as the univeriate case, $f_{X,Y}(x,y)$ must be non-negative, and must integrate to one: \n",
+    "$$\n",
+    " \\int\\int f_{X,Y}(x,y)dxdy=1\n",
+    "$$ \n",
     " \n",
-    " return(-sum(dnorm(Y, mean=mu, sd=sigma, log=TRUE)))\n",
-    "}"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "Note that we do something a bit different here (the \"`...`\" bit). We do it this way because we want to be able to use R's `optim()` function later.\n",
+    "##### Bivariate normal random variables\n",
+    "The support of a bivariate normal r.v. is the entire real number *plane*, or $\\Re^2$. In univariate normal we have two parameters $\\mu$ and $\\sigma^2$ which are both numbers. In bivariate normal we have the multivariate analogy of the two, but this time they are called the mean vector $\\boldsymbol{\\mu}=\\begin{pmatrix}\\mu_X \\\\ \\mu_Y \\end{pmatrix}$ and variance-covariance matrix $\\boldsymbol{\\Sigma}=\\begin{bmatrix}\\sigma_X^2 & \\rho \\sigma_X \\sigma_Y \\\\ \\rho \\sigma_X \\sigma_Y & \\sigma_Y^2 \\end{bmatrix}$. \n",
     "\n",
-    "The `dnorm()` function calculates the logged (the `log=TRUE` argument) probability of observing Y given mu, sigma and that X. \n",
+    "The entries of $\\boldsymbol{\\mu}$ and $\\boldsymbol{\\Sigma}$ are numbers. For instance, here we have the individual means and variances for $X$ and $Y$, and also $\\rho$ for the correlation between the two. Check the link below to visualise the joint pdf of a bivariate normal r.v.. \n",
     "\n",
-    "The negative sign on `sum()` is because the `optim()` function in R will minimize the negative log-likelihood, which is a sum: Recall that The log-likelihood of the parameters $\\theta$ being true given data x equals to the sum of the logged probability densities of observing the data x given parameters $\\theta$. We want to maximize this (log-) likelihood using `optim()`."
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "Let's generate some simulated data, assuming that: $\\beta_0=$ `b0`, $\\beta_1=$ `b1`, and $\\sigma=$ `sigma`. For this, we will generate random deviations to simulate sampling or measurement error around an otherwise perfect line of data values:"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 2,
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "set.seed(123)\n",
-    "n <- 30\n",
-    "b0 <- 10\n",
-    "b1 <- 3\n",
-    "sigma <- 2\n",
-    "X <- rnorm(n, mean=3, sd=7)\n",
-    "Y <- b0 + b1 * X + rnorm(n, mean=0, sd=sigma)\n",
-    "dat <- data.frame(X=X, Y=Y) # convert to a data frame"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "In the first line, we `set.seed()` to ensure that we can reproduce the results. The seed number you choose is the starting point used in the generation of a sequence of random numbers. No plot the \"data\":"
+    "http://socr.ucla.edu/htmls/HTML5/BivariateNormal/\n",
+    "\n",
+    "In general, for a $k$-dimensional multivariate normal, the mean vector is of length $k$, and the variance-covariance matrix is a $k$-by-$k$ symmetric and (semi)-postive definite matrix. Note that many applications rely on the decomposition of $\\boldsymbol{\\Sigma}$, such as Principal component analysis. \n",
+    "\n",
+    "#### Marginal distributions\n",
+    "Sometimes we are interested in one r.v. without referencing to the values of another. In this case the focus on finding the marginal distribution of the r.v. of interest. In a bivariate case with r.v. $X$ and $Y$ and their joint pdf $f_{X,Y}(x,y)$, the marginal pdf of $X$ is \n",
+    "$$\n",
+    " f_X(x)=\\int f_{X,Y}(x,y)dy$$ The integration along the $y$ axis is to marginalise out (get rid of) the uninterested r.v. $Y$. As a result, there will be no $y$ left in $f_X(x)$. Similarly, we can integrate along the other axis to find $f_Y(y)$. Note that the marginal pdf is indeed a pdf therefore the properties we discussed yesterday remain applicable. \n",
+    "\n",
+    "#### Conditional distributions\n",
+    "If the value of r.v. $Y$ is known (i.e. we know $Y=y$) then this may give additional information on another r.v. $X$. The distribution of interest here is the conditional distribution of $X$ given $Y$: \n",
+    "$$\n",
+    " f_{X|Y}(x|y)=\\frac{f_{X,Y}(x,y)}{f_Y(y)}$$ \n",
+    "We can imagine $f_{X|Y}(x|y)$ as a slice of the joint pdf at $Y=y$ after normalisation. Of course we can find the conditional of $Y|X$ from the joint and the marginal of $X$. The following relationship is established: $$\n",
+    "     f_{X|Y}(x|y)f_Y(y)=f_{X,Y}(x,y)=f_{Y|X}(y|x)f_X(x)\n",
+    "$$ \n",
+    "I hope some of you will notice that this is Bayes' theorem. I trust that you will be exposed to the theorem and its applications next week hence I shall not go beyond this. The key here is learn how we can obtain one distribution from the others via the \"joint = marginal x conditional\" relationship. \n",
+    "\n",
+    "### Expectation and covariance\n",
+    "As before, we can calculate expectations from the joint, conditional, or marginal distributions. With multiple r.v. come with more rules. \n",
+    "\n",
+    "#### Law of total expectation\n",
+    "\n",
+    "Given two r.v. $X$ and $Y$, $$\n",
+    "     E[Y]=E[E(Y|X)]\n",
+    "$$ \n",
+    "You first get the conditional expectation before taking another (outer) expectation to obtain the marginal expectation of $Y$. \n",
+    "\n",
+    "#### Law of total variance$$\n",
+    "     Var[Y]=E[Var(Y|X)]+Var[E(Y|X)]\n",
+    "$$ \n",
+    "which can be easily derived from the law of total expectation above. This is also called the \"Eve's formula\". \n",
+    "\n",
+    "#### Covariance and correlation\n",
+    "\n",
+    "Covariance measures the joint variability of a pair of r.v.. Given $X$ and $Y$, $$\n",
+    "     cov[X,Y]=E[XY]-E[X]E[Y]\n",
+    "$$ \n",
+    "where $E[XY]=\\int \\int xyf_{X,Y}(x,y)dxdy$. \n",
+    "\n",
+    "The correlation is the normalised measure describing the *linear* association between a pair of r.v.: \n",
+    "$$\n",
+    " corr[X,Y]=\\frac{cov[X,Y]}{Var[X]Var[Y]}$$ which is always bounded between -1 and +1. Note that only linear association is captured by correlation. A pair of r.v. can have zero correlation but are perfectly \"related\" (e.g. they go around a circle). \n",
+    "\n",
+    "Yesterday we mentioned that expectation is linear, that is, $E[X+Y]=E[X]+E[Y]$. This is true regardless of their correlation. The same cannot be said for variance:$$\n",
+    "     Var[aX+bY]=a^2Var[X]+b^2Var[Y]+2abcov[X,Y]\n",
+    "$$ \n",
+    "for some real numbers $a$ and $b$. \n",
+    "\n",
+    "### Independence\n",
+    "Independence is the strongest assumption in statistics as there is no way to test for it in real world. How can one confirm the toss of the first coin has nothing to do with the second? How can one be so certain that my action here will have zero influence to that by another person 1000 km away? Two events are independent if the occurrence of one does not affect the occurrence of another. \n",
+    "\n",
+    "If $X$ and $Y$ are independent then $corr[X,Y]=0$, but the reverse in not always true. In general $corr[X,Y]=0$ does not imply independence expect for some known cases (e.g. in multivariate normal). In fact, the assumption of independence is so strong that it guarantees $corr[g(x), h(y)]=0$ for all real functions $g$ and $h$ you can possibly imagine. \n",
+    "\n",
+    "#### Joint probability density functions under independence\n",
+    "$X$ and $Y$ are independent if and only if their joint pdf is the product of their marginals: \n",
+    "$$\n",
+    " f_{X,Y}(x,y)=f_X(x)f_Y(y)$$ \n",
+    "### Interval\n",
+    "So far we have been discussing the properties of r.v., calculating probabilities and expectations etc. based on some given assumptions and fixed parameter value. A typical question would involve calculating the probability that 0, 1, 2 buses will arrive in the next unit of time. For example, if we assume the arrival of buses $X$ follow a Poisson distribution with $\\lambda=3$, then\n",
+    "$$\n",
+    " f_X(x, \\lambda=3)=\\frac{\\lambda^xe^{-\\lambda}}{x!}=\\frac{3^xe^{-3}}{x!}$$ is a function of $x$ and a valid pmf. With known $/lambda$, we can calculate those probabilities by substituting $x=0$, $x=1$, and so on:"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 3,
-   "metadata": {},
+   "execution_count": 6,
+   "id": "818507eb-b962-4625-8486-b4f7495dce7c",
+   "metadata": {
+    "editable": true,
+    "slideshow": {
+     "slide_type": ""
+    },
+    "tags": []
+   },
    "outputs": [
     {
      "data": {
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G6kU99OvP3b/G3PVe8X45HcgpBwXOaT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\nAABJRU5ErkJggg==",
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pU1i9XHDtO5MDkjJORJ6JDaTneX57ZT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\nNVdXjDAAAAAASUVORK5CYII=",
       "text/plain": [
-       "plot without title"
+       "Plot with title “pmf of Poisson with lambda=3”"
       ]
      },
      "metadata": {
@@ -170,56 +367,46 @@
     }
    ],
    "source": [
-    "plot(X, Y)"
+    "probability <- dpois(0:15, lambda=3)\n",
+    "barplot(probability, space=1, beside=F, xlab='x', ylab='probability', main='pmf of Poisson with lambda=3')\n",
+    "axis(1, at=seq(1, 31, 2)+0.5, labels=0:15)"
    ]
   },
   {
    "cell_type": "markdown",
-   "metadata": {},
+   "id": "7822f4c9-ed81-4378-8de3-d189620f914a",
+   "metadata": {
+    "editable": true,
+    "slideshow": {
+     "slide_type": ""
+    },
+    "tags": []
+   },
    "source": [
-    "### Likelihood profile\n",
+    "From the pmf plot we know that $Pr(X=0)=0.0497$ and $Pr(X=1)=0.149$, and so on. Thur far there is no observation. We are still working out the probabilities of some potential outcomes inside our brain. We are still waiting for our bus. \n",
     "\n",
-    "For now, let's assume that we know what $\\beta_1$ is. Let's build a likelihood profile for the simulated data:"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 5,
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "N <- 50\n",
-    "b0s <- seq(5, 15, length=N)\n",
-    "mynll <- rep(NA, length=50)\n",
-    "for(i in 1:N){\n",
-    " mynll[i] <- nll.slr(par=c(b0s[i],b1), dat=dat, sigma=sigma)\n",
-    "}"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "That is, we calculate the negative log-likelihood for fixed b1, across a range (5 - 15) of b0. "
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "Now plot the profile:"
+    "Now, the tide has turned that we actually have some data! Say we observed 3 buses within a unit time. This time we have $x=3$, but $\\lambda$ is unknown. From the same Poisson \"function\", \n",
+    "$$\n",
+    " f_X(x=3, \\lambda)=\\frac{\\lambda^xe^{-\\lambda}}{x!}=\\frac{\\lambda^3e^{-\\lambda}}{3!}$$ it becomes a function of $\\lambda$ once the data is observed. One can plot this $f_X(x=3, \\lambda)$ against $\\lambda$, it is no longer a pmf (previously we plot it against $x$). By doing that, we are asking \"what is the proability of seeing 3 buses if $\\lambda=1$?\", and what if $\\lambda=1.5$? And so on. "
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 6,
-   "metadata": {},
+   "execution_count": 2,
+   "id": "da96450c-e95c-458a-a320-0c4f4d40f18b",
+   "metadata": {
+    "editable": true,
+    "slideshow": {
+     "slide_type": ""
+    },
+    "tags": []
+   },
    "outputs": [
     {
      "data": {
-      "image/png": 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V9++UU6BAAACGPYKV6jRo0aNGiwevVq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8u9y1659byOn1pWs9oLou2nO0jH4Ayt/Rcp+CHtcbMVkCzlG/sqZJ1rmBhPFyuj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\nAINEJIBBIhLAIBEJYJCIBDBIRAL+H8ciNG8Vcs5bAAAAAElFTkSuQmCC",
       "text/plain": [
-       "plot without title"
+       "Plot with title “this is NOT a pdf/pmf”"
       ]
      },
      "metadata": {
@@ -232,65 +419,84 @@
     }
    ],
    "source": [
-    "plot(b0s, mynll, type=\"l\")\n",
-    "abline(v=b0, col=2)\n",
-    "abline(v=b0s[which.min(mynll)], col=3)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "The true value for b0 (10) is the red line, while the value that minimizes the log-likelihood (i.e., maximizes the negative log-likelihood) is the green line. These are not the same because maximum likelihood is providing an * estimate * of the true value given the measurement errors (that we ourselves generated in tgis synthetic dataset). "
+    "plot(seq(0.1, 15, 0.01), dpois(3, lambda=seq(0.1, 15, 0.01)), type='l', lwd=2, \n",
+    "     xlab='lambda', ylab='robability of seeing 3 buses at this lambda value', main='this is NOT a pdf/pmf')"
    ]
   },
   {
    "cell_type": "markdown",
-   "metadata": {},
+   "id": "770e356e-8af8-4e4f-aa71-8113a913acc3",
+   "metadata": {
+    "editable": true,
+    "slideshow": {
+     "slide_type": ""
+    },
+    "tags": []
+   },
    "source": [
-    "(MLE-LikelihoodSurface)=\n",
-    "### Likelihood surface\n",
+    "Essentially we are making inference on the unknown parameter from our observation. In the remaining sections of this notebook, we will formally introduce the likelihood framework for statistical inference. Welcome to the world of Statistics. \n",
+    "\n",
+    "### Maximum Likelihood Estimation\n",
+    "Many said Maximum Likelihood Estimation (MLE) was invented by Sir Ronald Fisher, but I (as a statistician and geneticist many degrees inferior to Fisher) argue that such idea needs no invention but rather has been embedded in everybody's mind since the beginning of civilisation. I sincerely hope that by the end of this week you will appreciate MLE as a collection of methods who share a common belief towards how the \"best parameters\" should behave. \n",
+    "\n",
+    "A distribution of a r.v., or a statistical model comes with parameters. When a *dataset* is collected, and a statistical *model* is proposed, MLE provides a set of rules to find the best estimates of the associated *parameters*. In words, MLE aims to find the parameter values that make the observed dataset most \"probable\". \n",
     "\n",
-    "If we wanted to estimate both $\\beta_0$ and $\\beta_1$ (two parameters), we need to deal with a two-dimensional maximum likelihood surface. The simplest approach is to do a *grid search* to find this likelihood surface."
+    "The triplets: data, model, parameters. \n",
+    "\n",
+    "#### Likelihood function\n",
+    "To quantify how \"probable\" a paramter value is in producing our observed data we introduce the likelihood function $L(\\underline{\\theta})$. From now on we use $\\underline{\\theta}$ to denote a vector of parameters simply for generalisation (and similarly $\\underline{x}$ for a vector of data). \n",
+    "\n",
+    "By definition, the likelihood function is the joint density (pdf) of our observation $\\underline{x}$:\n",
+    "$$\n",
+    " L(\\underline{\\theta})=L(\\underline{\\theta}|\\underline{x})=f(\\underline{x}|\\underline{\\theta})=f(x_1, x_2, ..., x_n|\\underline{\\theta})$$ \n",
+    "Once $\\underline{x}$ is observed, you may imagine that $\\underline{x}$ turn into real numbers, and $L(\\underline{\\theta}|\\underline{x})$ is a function of $\\underline{\\theta}$ only. We can evaluate $L(\\underline{\\theta}|\\underline{x})$ along $\\underline{\\theta}$, and find a $\\underline{\\hat{\\theta}}$ that maximises the function $L(\\underline{\\theta}|\\underline{x})$. This is the spirit of MLE. \n",
+    "\n",
+    "#### Independent observations and log-likelihood\n",
+    "The likelihood function is the joint pdf of our observations. If they are independent, then the joint pdf becomes the product of univariate pdfs: \n",
+    "$$\n",
+    " L(\\underline{\\theta}|\\underline{x})=f(x_1, x_2, ..., x_n|\\underline{\\theta})$$ $$\n",
+    " =f_{X_1}(x_1)f_{X_2}(x_2)...f_{X_n}(x_n)$$ which streamlines the construction of the likelihood function. \n",
+    "\n",
+    "Besides, many prefers to work on the log-likelihood function $l(\\underline{\\theta}|\\underline{x})=\\ln(L(\\underline{\\theta}|\\underline{x}))$, as the product of pdfs immediately becomes the sum of log-pdfs. Both likelihood and log-likelihood functions attain their maximums at the same $\\underline{\\hat{\\theta}}$, because log is a monotonoic monotonic (also non-decreasing) function. \n",
+    "\n",
+    "In MLE, we treat parameters as fixed but unknown quantities to be estimated. We are inferring parameters, not the probability of hitting a particular outcome. The likelihood function is not a pdf hence does not integrate to one. It is a function of the parameters. \n",
+    "\n",
+    "#### Coin tossing example (in R)\n",
+    "Assume we obtain $y$ heads from $n$ independent tosses. By definition, the likelihood function is the joint pmf of these $n$ tosses, which looks like a binomial distribution: \n",
+    "$$\n",
+    " L(p|y)=C_y^np^y(1-p)^{n-y}$$ \n",
+    "After the experiment we observed 7 heads from 10 tosses. Let us put $y=7$ and $n=3$ into the likelihood function:\n",
+    "$$\n",
+    " L(p)=C^{10}_7p^7(1-p)^3$$ We can rewrite this function in R. I cannot stress enough that the likelihood is a function of the parameter, as seen from \n",
+    "`<-function(p)\n",
+    "`. We then plot the likelihood function against a range of values of $p$. Pay attention to the parameter space: $p$ is from Bernoulli hence it has to be bounded between 0 and 1. The second plot shows the log-likelihood function. "
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 7,
+   "execution_count": 3,
+   "id": "994a137f-b94c-437a-ae47-4b79cc77916c",
    "metadata": {
-    "scrolled": true
+    "editable": true,
+    "slideshow": {
+     "slide_type": ""
+    },
+    "tags": []
    },
    "outputs": [
     {
      "data": {
       "text/html": [
-       "<table>\n",
-       "<caption>A matrix: 2 × 2 of type dbl</caption>\n",
-       "<tbody>\n",
-       "\t<tr><td>10.00000</td><td>3.00</td></tr>\n",
-       "\t<tr><td>10.48485</td><td>2.96</td></tr>\n",
-       "</tbody>\n",
-       "</table>\n"
+       "8.748e-06"
       ],
       "text/latex": [
-       "A matrix: 2 × 2 of type dbl\n",
-       "\\begin{tabular}{ll}\n",
-       "\t 10.00000 & 3.00\\\\\n",
-       "\t 10.48485 & 2.96\\\\\n",
-       "\\end{tabular}\n"
+       "8.748e-06"
       ],
       "text/markdown": [
-       "\n",
-       "A matrix: 2 × 2 of type dbl\n",
-       "\n",
-       "| 10.00000 | 3.00 |\n",
-       "| 10.48485 | 2.96 |\n",
-       "\n"
+       "8.748e-06"
       ],
       "text/plain": [
-       "     [,1]     [,2]\n",
-       "[1,] 10.00000 3.00\n",
-       "[2,] 10.48485 2.96"
+       "[1] 8.748e-06"
       ]
      },
      "metadata": {},
@@ -298,7 +504,7 @@
     },
     {
      "data": {
-      "image/png": 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SA0QdjB2xxNSQ6BMA/9B/gbYQcfs7ca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ysrH3nkkffee6/B3x9GUl5e3qRJk4SE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\nYII=",
       "text/plain": [
        "plot without title"
       ]
@@ -313,233 +519,120 @@
     }
    ],
    "source": [
-    "N0 <- 100\n",
-    "N1 <- 101\n",
-    "b0s <- seq(7,12, length=N0)\n",
-    "b1s <- seq(1,5, length=N1)\n",
-    "\n",
-    "mynll <- matrix(NA, nrow=N0, ncol=N1)\n",
-    "for(i in 1:N0){\n",
-    " for(j in 1:N1) mynll[i,j] <- nll.slr(par=c(b0s[i],b1s[j]), dat=dat, sigma=sigma)\n",
+    "# WRITE DOWN THE LIKELIHOOD FUNCTION\n",
+    "binomial.likelihood<-function(p){\n",
+    "choose(10,7)*p^7*(1-p)^3\n",
     "}\n",
-    "\n",
-    "ww <- which(mynll==min(mynll), arr.ind=TRUE)\n",
-    "\n",
-    "b0.est <- b0s[ww[1]]\n",
-    "b1.est <- b1s[ww[2]]\n",
-    "rbind(c(b0, b1), c(b0.est, b1.est))\n",
-    "\n",
-    "filled.contour(x = b0s, y = b1s, z= mynll, col=heat.colors(21), \n",
-    "    plot.axes = {axis(1); axis(2); points(b0,b1, pch=21); \n",
-    "       points(b0.est, b1.est, pch=8, cex=1.5); xlab=\"b0\"; ylab=\"b1\"})"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "There is a lot going on here. Make sure you ask one of us if some of the code does not make sense!\n",
-    "\n",
-    "Again, note that the true parameter combination (asterisk) and the one what maximizes the negative log-likelihood (circle) are different."
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "### Conditional Likelihood\n",
-    "We can also look at the conditional surfaces (i.e., we look at the slice around whatever the best estimate is for the other parameter):"
+    "# LET US CALCULATE THE LIKELIHOOD VALUE AT p=0.1\n",
+    "binomial.likelihood(p=0.1)\n",
+    "# YOU GOT SOMETHING AROUND 8.748e-06, RIGHT?\n",
+    "# PLOT THE LIKELIHOOD FUNCTION FOR A RANGE OF p\n",
+    "p<-seq(0, 1, 0.01)\n",
+    "likelihood.values<-binomial.likelihood(p)\n",
+    "plot(p, likelihood.values, ylab='likelihood', type='l', lwd=2)\n",
+    "abline(v=0.7, col='red', lty=2, lwd=2)"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 60,
-   "metadata": {},
+   "execution_count": 4,
+   "id": "34724b80-d6c3-4376-bb1c-7782fbdc8b7f",
+   "metadata": {
+    "editable": true,
+    "slideshow": {
+     "slide_type": ""
+    },
+    "tags": []
+   },
    "outputs": [
     {
      "data": {
-      "image/png": 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Idujg8M9LgFaAR7YvuchMSumZn4KDDE4UIvYvV2nG3UEj+58kzEXEkYIe0GO+YT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\n16pftcQ5/vqKdrE2s3K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TqU724vimJn2Sh2gAYYjcbQ0NA1a9YY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\n9f7RIlTCdgAAAABJRU5ErkJggg==",
       "text/plain": [
        "plot without title"
       ]
      },
      "metadata": {
       "image/png": {
-       "height": 360,
-       "width": 300
+       "height": 420,
+       "width": 420
       }
      },
      "output_type": "display_data"
     }
    ],
    "source": [
-    "par(mfrow=c(1,2), bty=\"n\")\n",
-    "plot(b0s, mynll[,ww[2]], type=\"l\", xlab=\"b0\", ylab=\"NLL\")\n",
-    "plot(b1s, mynll[ww[1],], type=\"l\", xlab=\"b1\", ylab=\"NLL\")"
+    "# LOG-LIKELIHOOD FUNCTION\n",
+    "log.binomial.likelihood<-function(p){\n",
+    "log(binomial.likelihood(p=p))\n",
+    "}\n",
+    "# PLOT THE LOG-LIKELIHOOD\n",
+    "p<-seq(0, 1, 0.01)\n",
+    "log.likelihood.values<-log.binomial.likelihood(p)\n",
+    "plot(p, log.likelihood.values, ylab='log-likelihood', type='l', lwd=2)\n",
+    "abline(v=0.7, col='red', lty=2, lwd=2)"
    ]
   },
   {
    "cell_type": "markdown",
-   "metadata": {},
+   "id": "0e4fcd2b-1227-4898-872c-0ee28439a2f0",
+   "metadata": {
+    "editable": true,
+    "slideshow": {
+     "slide_type": ""
+    },
+    "tags": []
+   },
    "source": [
-    "## Alternatives to Grid Search\n",
-    "\n",
-    "There are many alternative methods to grid searches. Since we are seeking to minimize an arbitrary function (the negative log likelihood) we typically use a descent method to perform general optimization.\n",
-    "\n",
-    "There are lots of options implemented in the `optim`function in R. We won't go into the details of these methods, due to time constraints. However, typically one would most commonly use:\n",
-    "\n",
-    " * Brent's method: for 1-D search within a bounding box, only\n",
-    " * L-BFGS-B (limited-memory Broyden–Fletcher–Goldfarb–Shanno algorithm with bounding box constraints): a quasi-Newton method, used for higher dimensions, when you want to be able to put simple limits on your search area. \n",
-    " \n",
-    "\n",
-    "## Maximum Likelihood using `optim()`\n",
+    "The next step is to find value of $p$ such that $L(p)$ is maximised. It appears that the peak is at 0.7, and we say $\\hat{p}=0.7$ is our maximum likelihood estimate. \n",
     "\n",
-    "We can now do the fitting. This involves optimization (to find the appropriate parameter values that achieve the maximum of the likelihood surface above). For this, we will use R's versatile `optim()` function.\n",
-    "\n",
-    "The first argument for `optim()` is the function that you want to minimize, and the second is a vector of starting values for your parameters (as always, do a`?optim`). After the main arguments, you can add what you need to evaluate your function (e.g. `sigma` ). The addtional argument sigma can be \"fed\" to `nll.slr` because we use the `...` convention when defining it."
+    "Beyond eyeballing, we can use R's optimisation routines to find the maixmum/minimum of a function. For univariate (one-parameter) case, we can use \n",
+    "`optimize()\n",
+    "`:"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 61,
+   "execution_count": 5,
+   "id": "e8fa1a5d-53f8-4996-99d7-4b14eb7580b7",
    "metadata": {
-    "scrolled": true
+    "editable": true,
+    "slideshow": {
+     "slide_type": ""
+    },
+    "tags": []
    },
    "outputs": [
     {
      "data": {
       "text/html": [
        "<dl>\n",
-       "\t<dt>$par</dt>\n",
-       "\t\t<dd><style>\n",
-       ".list-inline {list-style: none; margin:0; padding: 0}\n",
-       ".list-inline>li {display: inline-block}\n",
-       ".list-inline>li:not(:last-child)::after {content: \"\\00b7\"; padding: 0 .5ex}\n",
-       "</style>\n",
-       "<ol class=list-inline><li>10.4589351280817</li><li>2.96170447551098</li></ol>\n",
-       "</dd>\n",
-       "\t<dt>$value</dt>\n",
-       "\t\t<dd>58.2247252772924</dd>\n",
-       "\t<dt>$counts</dt>\n",
-       "\t\t<dd><style>\n",
-       ".dl-inline {width: auto; margin:0; padding: 0}\n",
-       ".dl-inline>dt, .dl-inline>dd {float: none; width: auto; display: inline-block}\n",
-       ".dl-inline>dt::after {content: \":\\0020\"; padding-right: .5ex}\n",
-       ".dl-inline>dt:not(:first-of-type) {padding-left: .5ex}\n",
-       "</style><dl class=dl-inline><dt>function</dt><dd>12</dd><dt>gradient</dt><dd>12</dd></dl>\n",
-       "</dd>\n",
-       "\t<dt>$convergence</dt>\n",
-       "\t\t<dd>0</dd>\n",
-       "\t<dt>$message</dt>\n",
-       "\t\t<dd>'CONVERGENCE: REL_REDUCTION_OF_F &lt;= FACTR*EPSMCH'</dd>\n",
+       "\t<dt>$maximum</dt>\n",
+       "\t\t<dd>0.699984294307121</dd>\n",
+       "\t<dt>$objective</dt>\n",
+       "\t\t<dd>0.266827930432933</dd>\n",
        "</dl>\n"
       ],
       "text/latex": [
        "\\begin{description}\n",
-       "\\item[\\$par] \\begin{enumerate*}\n",
-       "\\item 10.4589351280817\n",
-       "\\item 2.96170447551098\n",
-       "\\end{enumerate*}\n",
-       "\n",
-       "\\item[\\$value] 58.2247252772924\n",
-       "\\item[\\$counts] \\begin{description*}\n",
-       "\\item[function] 12\n",
-       "\\item[gradient] 12\n",
-       "\\end{description*}\n",
-       "\n",
-       "\\item[\\$convergence] 0\n",
-       "\\item[\\$message] 'CONVERGENCE: REL\\_REDUCTION\\_OF\\_F <= FACTR*EPSMCH'\n",
+       "\\item[\\$maximum] 0.699984294307121\n",
+       "\\item[\\$objective] 0.266827930432933\n",
        "\\end{description}\n"
       ],
       "text/markdown": [
-       "$par\n",
-       ":   1. 10.4589351280817\n",
-       "2. 2.96170447551098\n",
-       "\n",
-       "\n",
-       "\n",
-       "$value\n",
-       ":   58.2247252772924\n",
-       "$counts\n",
-       ":   function\n",
-       ":   12gradient\n",
-       ":   12\n",
-       "\n",
-       "\n",
-       "$convergence\n",
-       ":   0\n",
-       "$message\n",
-       ":   'CONVERGENCE: REL_REDUCTION_OF_F &lt;= FACTR*EPSMCH'\n",
+       "$maximum\n",
+       ":   0.699984294307121\n",
+       "$objective\n",
+       ":   0.266827930432933\n",
        "\n",
        "\n"
       ],
       "text/plain": [
-       "$par\n",
-       "[1] 10.458935  2.961704\n",
-       "\n",
-       "$value\n",
-       "[1] 58.22473\n",
-       "\n",
-       "$counts\n",
-       "function gradient \n",
-       "      12       12 \n",
-       "\n",
-       "$convergence\n",
-       "[1] 0\n",
-       "\n",
-       "$message\n",
-       "[1] \"CONVERGENCE: REL_REDUCTION_OF_F <= FACTR*EPSMCH\"\n"
-      ]
-     },
-     "metadata": {},
-     "output_type": "display_data"
-    }
-   ],
-   "source": [
-    "fit <- optim(nll.slr, par=c(2, 1), method=\"L-BFGS-B\", ## this is a n-D method\n",
-    "    lower=-Inf, upper=Inf, dat=dat, sigma=sigma)\n",
-    "\n",
-    "fit"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "Easy as pie (once you have the recipe)! We can also fit sigma as the same time if we want:"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 62,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/html": [
-       "<style>\n",
-       ".list-inline {list-style: none; margin:0; padding: 0}\n",
-       ".list-inline>li {display: inline-block}\n",
-       ".list-inline>li:not(:last-child)::after {content: \"\\00b7\"; padding: 0 .5ex}\n",
-       "</style>\n",
-       "<ol class=list-inline><li>10.4589449542964</li><li>2.96170371229526</li><li>1.62168936031414</li></ol>\n"
-      ],
-      "text/latex": [
-       "\\begin{enumerate*}\n",
-       "\\item 10.4589449542964\n",
-       "\\item 2.96170371229526\n",
-       "\\item 1.62168936031414\n",
-       "\\end{enumerate*}\n"
-      ],
-      "text/markdown": [
-       "1. 10.4589449542964\n",
-       "2. 2.96170371229526\n",
-       "3. 1.62168936031414\n",
+       "$maximum\n",
+       "[1] 0.6999843\n",
        "\n",
-       "\n"
-      ],
-      "text/plain": [
-       "[1] 10.458945  2.961704  1.621689"
+       "$objective\n",
+       "[1] 0.2668279\n"
       ]
      },
      "metadata": {},
@@ -547,225 +640,173 @@
     }
    ],
    "source": [
-    "fit <- optim(nll.slr, par=c(2, 1, 5), method=\"L-BFGS-B\", ## this is a n-D method\n",
-    "    lower=c(-Inf, -Inf, 0.1), upper=Inf, dat=dat, sigma=NA)\n",
-    "fit$par"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "The starting values (b0 = 2, b1 = 1, sigma = 5) need to be assigned as we would do for NLLS. Also note that much like NLLS, we have bounded the parameters. The exact starting values are not too important in this case (try changing them see what happens)."
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "Now visualize the fit:"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 63,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "image/png": 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ebOg7zPN7FaLSMUyuYHWbZtwXVMc4Yi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\nlr8lh+QAAAAASUVORK5CYII=",
-      "text/plain": [
-       "plot without title"
-      ]
-     },
-     "metadata": {
-      "image/png": {
-       "height": 360,
-       "width": 300
-      }
-     },
-     "output_type": "display_data"
-    }
-   ],
-   "source": [
-    "plot(X, Y)\n",
-    "abline(a=fit$par[1], b=fit$par[2], col=2, lwd=2)"
+    "optimize(binomial.likelihood, interval=c(0,1), maximum=TRUE)"
    ]
   },
   {
    "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "### Confidence intervals\n",
-    "\n",
-    "The joint distribution of the MLEs are asymptotically Normally distributed. Given this, if you are minimizing the negative log likelihood (NLL) then the covariance matrix of the estimates is (asymptotically) the inverse of the Hessian matrix. The Hessian matrix evalutes the second derivatives of the NLL (numerically here), which gives us information about the curvature the likelihood. Thus we can use the Hessian to estimate confidence intervals:"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 64,
+   "id": "dfeb8208-1f77-49e6-ab0d-37125eb0f5d1",
    "metadata": {
-    "scrolled": true
+    "editable": true,
+    "slideshow": {
+     "slide_type": ""
+    },
+    "tags": []
    },
-   "outputs": [
-    {
-     "data": {
-      "text/html": [
-       "<table>\n",
-       "<caption>A data.frame: 2 × 3</caption>\n",
-       "<thead>\n",
-       "\t<tr><th scope=col>value</th><th scope=col>upper</th><th scope=col>lower</th></tr>\n",
-       "\t<tr><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th></tr>\n",
-       "</thead>\n",
-       "<tbody>\n",
-       "\t<tr><td>10.458935</td><td>11.228565</td><td>9.689305</td></tr>\n",
-       "\t<tr><td> 2.961704</td><td> 3.067705</td><td>2.855704</td></tr>\n",
-       "</tbody>\n",
-       "</table>\n"
-      ],
-      "text/latex": [
-       "A data.frame: 2 × 3\n",
-       "\\begin{tabular}{lll}\n",
-       " value & upper & lower\\\\\n",
-       " <dbl> & <dbl> & <dbl>\\\\\n",
-       "\\hline\n",
-       "\t 10.458935 & 11.228565 & 9.689305\\\\\n",
-       "\t  2.961704 &  3.067705 & 2.855704\\\\\n",
-       "\\end{tabular}\n"
-      ],
-      "text/markdown": [
-       "\n",
-       "A data.frame: 2 × 3\n",
-       "\n",
-       "| value &lt;dbl&gt; | upper &lt;dbl&gt; | lower &lt;dbl&gt; |\n",
-       "|---|---|---|\n",
-       "| 10.458935 | 11.228565 | 9.689305 |\n",
-       "|  2.961704 |  3.067705 | 2.855704 |\n",
-       "\n"
-      ],
-      "text/plain": [
-       "  value     upper     lower   \n",
-       "1 10.458935 11.228565 9.689305\n",
-       "2  2.961704  3.067705 2.855704"
-      ]
-     },
-     "metadata": {},
-     "output_type": "display_data"
-    }
-   ],
    "source": [
-    "fit <- optim(nll.slr, par=c(2, 1), method=\"L-BFGS-B\", hessian=TRUE, lower=-Inf, upper=Inf, dat=dat, sigma=sigma)\n",
-    "\n",
-    "fisher_info <- solve(fit$hessian)\n",
-    "est_sigma <- sqrt(diag(fisher_info))\n",
-    "upper <- fit$par+1.96 * est_sigma\n",
-    "lower <- fit$par-1.96 * est_sigma\n",
-    "interval <- data.frame(value=fit$par, upper=upper, lower=lower)\n",
-    "interval"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "### Comparison to fitting with least squares\n",
     "\n",
-    "We can, of course, simply fit the model with lest squares using the `lm()` function:"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 65,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/html": [
-       "<table>\n",
-       "<caption>A matrix: 2 × 4 of type dbl</caption>\n",
-       "<thead>\n",
-       "\t<tr><th></th><th scope=col>Estimate</th><th scope=col>Std. Error</th><th scope=col>t value</th><th scope=col>Pr(&gt;|t|)</th></tr>\n",
-       "</thead>\n",
-       "<tbody>\n",
-       "\t<tr><th scope=row>(Intercept)</th><td>10.458936</td><td>0.32957007</td><td>31.73509</td><td>1.699822e-23</td></tr>\n",
-       "\t<tr><th scope=row>X</th><td> 2.961704</td><td>0.04539126</td><td>65.24834</td><td>3.874555e-32</td></tr>\n",
-       "</tbody>\n",
-       "</table>\n"
-      ],
-      "text/latex": [
-       "A matrix: 2 × 4 of type dbl\n",
-       "\\begin{tabular}{r|llll}\n",
-       "  & Estimate & Std. Error & t value & Pr(>\\textbar{}t\\textbar{})\\\\\n",
-       "\\hline\n",
-       "\t(Intercept) & 10.458936 & 0.32957007 & 31.73509 & 1.699822e-23\\\\\n",
-       "\tX &  2.961704 & 0.04539126 & 65.24834 & 3.874555e-32\\\\\n",
-       "\\end{tabular}\n"
-      ],
-      "text/markdown": [
-       "\n",
-       "A matrix: 2 × 4 of type dbl\n",
-       "\n",
-       "| <!--/--> | Estimate | Std. Error | t value | Pr(&gt;|t|) |\n",
-       "|---|---|---|---|---|\n",
-       "| (Intercept) | 10.458936 | 0.32957007 | 31.73509 | 1.699822e-23 |\n",
-       "| X |  2.961704 | 0.04539126 | 65.24834 | 3.874555e-32 |\n",
-       "\n"
-      ],
-      "text/plain": [
-       "            Estimate  Std. Error t value  Pr(>|t|)    \n",
-       "(Intercept) 10.458936 0.32957007 31.73509 1.699822e-23\n",
-       "X            2.961704 0.04539126 65.24834 3.874555e-32"
-      ]
-     },
-     "metadata": {},
-     "output_type": "display_data"
-    }
-   ],
-   "source": [
-    "lmfit <- lm(Y~X)\n",
+    "`\\$optimize()\n",
+    "` returns the parameter value at which the function attains its maximum, where the \n",
+    "`\\$objective\n",
+    "` is the maximised function value. \n",
     "\n",
-    "summary(lmfit)$coeff"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "The estimates we get using `optim()` are almost identical to the estimates that we obtain here, and the standard errors on the intercept and slope are very similar to those we calculated from the Hessian (est_sigma= `r est_sigma`). "
+    "#### Coin tossing example (by hand)\n",
+    "For a more general case with $y$ heads from $n$ independent tosses the likelihood function is:\n",
+    "$$\n",
+    " L(p)=C_y^np^y(1-p)^{n-y}$$ To maximise a function means to find the first derivative, then find the point with zero slope. Of course there are other conditions to meet (e.g. the second derivative) for the global maximum. Here, let us work on the log-likelihood:\n",
+    "$$\n",
+    " l(p)=\\ln(L(p))=\\ln(C_y^n)+y\\ln(p)+(n-y)\\ln(1-p)$$ Next, we differentiate $l(p)$ *with respect to $p$*. Note that the first term $\\ln(C_y^n)$ does not contain $p$ thus is treated as a constant:\n",
+    "$$\n",
+    " l'(p)=0+y\\frac{1}{p}+(n-y)\\frac{-1}{1-p}$$ Next, we find a $\\hat{p}$ such that $l'(\\hat{p})=0$:\n",
+    "$$\n",
+    " \\hat{p}=\\frac{y}{n}$$ and we say this is the MLE for the (fixed but unknown) parameter $p$. \n",
+    "\n",
+    "#### i.i.d. Normal samples with unknown $\\mu$\n",
+    "Suppose we have $X_1, X_2, ..., X_n$ i.i.d. samples from $N(\\mu, 1)$. Variance is known but $\\mu$ is the parameter to be estimated. By definition, the likelihood is a function of $\\mu$, and is the joint pdf of our samples:\n",
+    "$$\n",
+    " L(\\mu)=f(x_1, x_2, ..., x_n)$$ Here $f$ is a joint (higher-dimensional) pdf. As these samples are independent, the joint pdf becomes the product of individual pdfs:\n",
+    "$$\n",
+    " L(\\mu)=f_{X_1}(x_1)f_{X_2}(x_2)...f_{X_n}(x_n)$$ Note that $f_{X_i}$ are individual (one-dimensional) pdfs. Next, we make use of the fact that they are i.i.d. normal: \n",
+    "$$\n",
+    " L(\\mu)=\\prod_{i=1}^n\\frac{1}{\\sqrt{2\\pi}}e^{\\frac{(x_i-\\mu)^2}{2}})$$ $$\n",
+    " =(\\frac{1}{\\sqrt{2\\pi}})^ne^{\\frac{1}{2}\\sum_{i=1}^n(x_i-\\mu)^2}$$ The log-likelihood function is:\n",
+    "$$\n",
+    " l(\\mu)=constant-\\frac{1}{2}\\sum_{i=1}^n(x_i-\\mu)^2$$ Next, differentiate it w.r.t. $\\mu$:\n",
+    "$$\n",
+    " l'(\\mu)=0-\\frac{1}{2}[-2\\sum_{i=1}^n(x_i-\\mu)]$$ Find a value of $\\hat{\\mu}$ such that $l'(\\hat{\\mu})=0$. That is to solve the following equation:\n",
+    "$$\n",
+    " \\sum_{i=1}^n(x_i-\\hat{\\mu})=0$$ Rearranging the terms gives:\n",
+    "$$\n",
+    " \\hat{\\mu}=\\frac{\\sum_{i=1}^nx_i}{n}$$ And this is our MLE. \n",
+    "\n",
+    "#### i.i.d. Normal samples unknown $\\mu$ and $\\sigma^2$\n",
+    "With unknown $\\sigma^2$ the formulation of the log-likelihood function is the same as in the previous example but it is now a bivariate (two-paramter) function $l(\\mu, \\sigma^2)$. Because of this, the *partial* derivavtives $\\frac{\\partial l}{\\partial\\mu}$ and $\\frac{\\partial l}{\\partial\\sigma^2}$ need to be evaluated. A partial derivative is the derivative of a multivariate function with respect to one of the variables while treating the others as constant. At last, we need to find a pair of $(\\hat{\\mu}, \\hat{\\sigma^2})$ such that the partial derivatives are zero simultaneously. Again pay attention to the parameter space: $\\mu$ can be any real number, but $\\sigma^2$ (or $\\sigma$ itself) must be non-negative. I leave this as an exercise. "
    ]
   },
   {
    "cell_type": "markdown",
-   "metadata": {},
+   "id": "f5717bf0-8fad-48c7-be20-7790b1739144",
+   "metadata": {
+    "editable": true,
+    "slideshow": {
+     "slide_type": ""
+    },
+    "tags": []
+   },
    "source": [
-    "## Model Selection\n",
+    "## Theoretical guarantees\n",
+    "\n",
+    "<!-- More MLE examples: linear regression, general linearised regression (logistic and Poisson). \n",
+    "\n",
+    "Using <code>optim()</code>. \n",
+    "\n",
+    "Properties of ML estimators: asymptotically unbiased, asymptotically efficient, consistent, asymptotically normal, invariance. \n",
+    " -->\n",
+    "\n",
+    "### More MLE examples\n",
+    "\n",
+    "#### Linear regression\n",
+    "I hope we are all familiar with the simplest form of a linear regression. It comprises a vector of response $\\underline{x}$ and a vector of independent (or explanatory) variable $\\underline{x}$: \n",
+    "$$y_i=a+bx_i+\\epsilon_i$$\n",
+    "where $a$ is the intercept and $b$ is the slope. $i=1, 2, ..., n$. $\\epsilon_i$ is the error term, and in simple linear regression, $\\epsilon_i$ are assumed to be i.i.d. $N(0,\\sigma^2)$. \n",
+    "\n",
+    "Now we have identified the triplets required for parameter estimation: Our data $\\underline{x}$ and $\\underline{y}$. The three parameters of interest: $a$, $b$, and $\\sigma^2$. And finally the model, which is i.i.d. normal errors. If we rearrange the regression equation such that the error is the subject:\n",
+    "$$\\epsilon_i=y_i-a-bx_i$$\n",
+    "Then the likelihood becomes\n",
+    "$$L(\\underline{\\theta})=f(\\epsilon_1\\epsilon_2...\\epsilon_n)=\\prod_{i=1}^nf(\\epsilon_i)$$\n",
+    "The first $f$ is the joint density of all the error terms, and the second $f$ is the pdf of an individual error (which is normally distributed with a common variance). Now the problem has reverted back to the one we saw in #4.6 yesterday, that we need to find a set of $(\\hat{a}, \\hat{b}, \\hat{\\sigma^2})$ such that the likelihood is maximised. I probably would delegate this task to R, see today's practical on <code>recapture.csv</code>, also available in a separate notebook. In R, we can use the built-in <code>dnorm(y-a-b*x, mean=0, sd=sigma)</code> instead of writing the normal pdf explicitly. \n",
+    "\n",
+    "#### Logistic regression\n",
+    "Logistic regression belongs to the family of generalised linear models (GLM). It aims to relate a binary response to a set of explanatory variable(s). For example, in public health a typical binary response will be the state of the patients (dead/alive), or whether a parasite is absent or present in one's body. When I think of a binary variable, I immediately recall the Bernoulli r.v., whose outcome is either 0 or 1. In fact, logistic regression assumes that each binary outcome is a Bernoulli r.v. with its own $p_i$:\n",
+    "$$Y_i\\sim Bernoulli(p_i)$$\n",
+    "$i=1, 2, ..., n$. In addition, $p_i$ is influenced by the explanatory variable $x_i$. As a result, some will have a higher probability of success, depending on its relationship with $x_i$. Here I suggest the following form:\n",
+    "$$p_i=\\eta^{-1}(a+bx_i)$$\n",
+    "$a$ and $b$ are the coefficients, similar to the intercept and slope in linear regression. $(a+bx_i)$ is called the linear predictor. The remaining question is, what is $\\eta^{-1}$? \n",
+    "$$\\eta^{-1}=\\frac{e^{a+bx_i}}{1+e^{a+bx_i}}$$\n",
+    "We know from the Bernoulli r.v. that $p_i$ has to be bounded between 0 and 1, but $(a+bx_i)$ can be any real number (linear). That is why we call upon $\\eta^{-1}$ to map a real number to $[0, 1]$. $\\eta^{-1}$ is called the *expit* transformation, and its inverse $\\eta$ is *logit*, hence the name of the model. \n",
+    "\n",
+    "With the triplets identified we can proceed to find the ML estimates for $a$ and $b$. See <code>flowering.txt</code>, also available in a separate notebook. \n",
     "\n",
-    "You can use [AIC or BIC as you did in NLLS](#Comparing-models) using the likelihood you have calculated. \n",
+    "#### Poisson regression\n",
+    "Poisson regression is another GLM which is often used when the response are counts (e.g. number of mutations/crossovers). As its name suggests, it assumes each response follows a Poisson distribution with its own rate parameter $\\lambda_i$:\n",
+    "$$Y_i\\sim Poisson(\\lambda_i)$$\n",
+    "$i=1, 2, ..., n$. Similar to the logistic case, we need a function to link up $\\lambda_i$ with the linear predictor. The constraint here is that $\\lambda_i$ must be non-negative due to it being a rate. An appropriate function will be exponential: \n",
+    "$$\\lambda_i=e^{a+bx_i}$$\n",
+    "Note that the inverse of exponential is log. \n",
     "\n",
-    "You can also use the Likelihood Ratio Test (LRT).\n",
+    "In GLM, a link function provides the relationship between the lienar predictor and the mean of the distribution function. Logit and log are link functions in logistic and Poisson GLMs, respectively. I hope these examples help demystify GLMs and their model fitting via <code>glm(y~x, family=)</code>. \n",
     "\n",
-    "## Exercises <a id='MLE_Exercises'></a> \n",
+    "###. <code>optim()</code>\n",
+    "<code>optim()</code> is a generic optimisation routines for multivariate functions, similar to what <code>optimize()</code> does in univariate case. Here multivariate refers to the number of parameters rather than observations. It is a so powerful that its help file <code>?optim</code> provides more questions than answers. \n",
     "\n",
-    "Try MLE fitting for the allometric trait data example [above](#Allometric-scaling-of-traits). You will use the same data + functions that you used to practice fitting curves using non-linear least squares methods. You have two options here. The easier one is to convert the power law model to a straight line model by taking a log (explained the Allometry [Exercises](#Allom_Exercises). Specifically,\n",
+    "#### Inputs\n",
+    "It takes quite a few arguments, usually in the following order:\n",
+    "1) The mandatory <code>par=</code> vector specifies the initial condition for the search. If it is a $k$-dimensional function then a vector of length $k$ should be supplied. Avoid starting near the boundary of the parameter space. \n",
+    "2) Put the function name you wish to optimise under <code>fn=</code>. Mandatory.\n",
+    "3) <code>method=</code> instructs the optimisation algorithm to be used. The default is Nelder-Mead. The choice of algorithm can affect performance and numerical results. Another population option is <code>method='L-BFGS-B'</code> which takes a box-like constraint (see below).\n",
+    "4) The default algorithm imposes no constraints on the parameter space which is a double-edged sword. When <code>method='L-BFGS-B'</code> is chosen, then you must supply <code>lower=</code> and <code>upper=</code> as two vectors (with lengths equal to the number of parameters). This algorithm is useful when some parameters cannot go beyond a certain value (e.g. Poisson rates $\\lambda_i$ must be non-negative). \n",
+    "5) Other control options, such as tolerance, can be supplied to the control list <code>control=list((fnscale=-1))</code>. In particular, <code>fnscale=-1</code> means to maximise. The default is minimise. \n",
+    "6) <code>hessian=T</code> to return the Hessian matrix. Optional but useful. \n",
     "\n",
-    "(a) Using the [`nll.slr`](#Implementing-the-Likelihood-in-R) function as an example, write a function that calculates the negative log likelihood as a function of the parameters describing your trait and any additional parameters you need for an appropriate noise distribution (e.g., $\\sigma$ if you have normally distributed errors).\n",
+    "#### Outputs\n",
+    "It returns a big list: \n",
+    "1) <code>\\$par</code> is the parameter values that maximise the function. \n",
+    "2) <code>\\$value</code> returns the maximised function value.\n",
+    "3) The rest are for performance and convergence checking. If you have asked for the Hessian matrix, you may find it in the output as well. \n",
     "\n",
-    "(b) For at least one of your parameters plot a likelihood profile given your data, with the other parametes fixed.\n",
+    "There are other alternatives to <code>optim()</code>, such as <code>nlm()</code> and <code>nlminb</code>. External packages are available as well. \n",
     "\n",
-    "(c) Use the `optim` function to find the MLE of the same parameter and indicate this on your likelihood profile.\n",
+    "###. Properties of ML estimators\n",
+    "Below are the theoretical guarantees of ML estimators. They also justify why we are spending one whole week on likelihood. \n",
     "\n",
-    "(d) Obtain a confidence interval for your estimate.\n",
+    "#### ML estimators are asymptotically unbiased\n",
+    "If we repeat the experiment (and ML estimation) infinitely many times and obtain many $\\hat{\\theta}$, then the hypothetical average of this $ \\ hat {\\theta}$ is $\\theta$. When we talk of a hypothetical average we mean expectation: \n",
+    "$$E[\\hat{\\theta}]\\rightarrow \\theta$$\n",
+    "when $n\\rightarrow \\infty$. \n",
     "\n",
-    "A more challenging option is to fit the allometry data directly to the power law equation. You would need to assume a log-normal distribution for the errors instead of normal, in this case. "
+    "#### ML estimators are asymptotically efficient\n",
+    "Efficiency means the ML estimator $\\hat{\\theta}$ usually has a lower variance compared to the other estimators (what are the other estimators?). Since it has better use of the data, it produces narrower confidence intervals (C.I.). In particular, $Var[\\hat{\\theta}]$ reaches the theoretical lower bound when $n\\rightarrow \\infty$. \n",
+    "\n",
+    "#### ML estimators are consistent\n",
+    "The ML estimator $\\hat{\\theta}$ converges *in probability* to the true parameter $\\theta$ when $n\\rightarrow \\infty$. \n",
+    "\n",
+    "#### ML estimators are asymptotically normal\n",
+    "The ML estimator $\\hat{\\theta}$ is asymptotically distributed as normal with mean equals the true parameter $\\theta$. This is closely related to the central limit theorem, and this explains why the magic number 1.96 works in constructing C.I.. Have you ever wondered why a z-test is used in a <code>glm()</code>?\n",
+    "\n",
+    "#### The invariant principle of ML estimators\n",
+    "If $\\hat{\\theta}$ is the ML estimator for the parameter $\\theta$, then $g(\\hat{\\theta})$ is the ML estimator for $g(\\theta)$. Essentially we do not need to recalculate the ML estimator if the transformed parameter is of concern. "
    ]
   },
   {
    "cell_type": "markdown",
-   "metadata": {},
+   "id": "d9e66dc7-a0e5-4c56-a2b7-59719b47bff4",
+   "metadata": {
+    "editable": true,
+    "slideshow": {
+     "slide_type": ""
+    },
+    "tags": []
+   },
    "source": [
-    "Readings and Resources <a id='Readings'></a>\n",
-    "--------------------------------------------\n",
-    " * Bolker, B. Ecological models and data in R. (Princeton University Press, 2008). "
+    "# Readings and Resources <a id='Readings-MLE'></a>\n",
+    "\n",
+    "* Millar, [Maximum Likelihood Estimation and Inference](https://onlinelibrary.wiley.com/doi/book/10.1002/9780470094846)\n",
+    "   \n",
+    "* Crawley, [The R Book](https://onlinelibrary.wiley.com/doi/book/10.1002/9781118448908)\n",
+    "\n",
+    "* Hogg & Tanis, [Probability and Statistical Inference](https://faculty.ksu.edu.sa/sites/default/files/677_fr37hij.pdf)\n",
+    "\n",
+    "* Bolker, B. [Ecological models and data in R](https://ms.mcmaster.ca/~bolker/emdbook/book.pdf). (Princeton University Press, 2008)."
    ]
   }
  ],
@@ -781,43 +822,9 @@
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diff --git a/content/notebooks/test/MLE_ah.ipynb b/content/notebooks/test/MLE_ah.ipynb
new file mode 100644
index 00000000..b8765dde
--- /dev/null
+++ b/content/notebooks/test/MLE_ah.ipynb
@@ -0,0 +1,823 @@
+{
+ "cells": [
+  {
+   "cell_type": "code",
+   "execution_count": 1,
+   "metadata": {
+    "tags": [
+     "remove-cell"
+    ]
+   },
+   "outputs": [],
+   "source": [
+    "library(repr) ; options(repr.plot.width = 5, repr.plot.height = 6) # Change plot sizes (in cm)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "# Model Fitting using Maximum Likelihood"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Introduction\n",
+    "\n",
+    "\n",
+    "In this Chapter we will work through various examples of  model fitting  to biological data using Maximum Likelihood. It is recommended that you see this introductory [lecture](https://github.com/MulQuaBio/MQB/tree/main/content/lectures/EnE_Modelling_Intro) on model fitting in Ecology and Evolution. \n",
+    "\n",
+    "[Previously](./NLLS.ipynb), we learned how to fit a mathematical model/equation to data by using the Least Squares method (linear or nonlinear). That is, we choose the parameters of model being fitted (e.g., straight line) to minimize the sum of the squares of the residuals/errors around the fitted model. \n",
+    "\n",
+    "An alternative to minimizing the sum of squared errors is to find parameters to the function such that the * likelihood * of the parameters, given the data and the model, is maximized. Please see the [lectures](https://github.com/vectorbite/VBiTraining2/tree/master/lectures) for the theoretical background to the following examples.\n",
+    "\n",
+    "We will first implement the (negative log) likelihood for [simple linear regression (SLR)](./Regress.ipynb) in R. Recall that SLR assumes every observation in the dataset was generated by the model:\n",
+    "\n",
+    "$$\n",
+    "Y_i = \\beta_0 + \\beta_1 X_i + \\varepsilon_i, \\;\\;\\; \\varepsilon_i \\stackrel{\\mathrm{iid}}{\\sim} \\mathrm{N}(0, \\sigma^2)\n",
+    "$$\n",
+    "\n",
+    "That is, this is a model for the * conditional distribution * of $Y$ given $X$. The pdf for the normal distribution is given by\n",
+    "\n",
+    "$$\n",
+    "f(x) = \\frac{1}{\\sqrt{2\\sigma^2 \\pi}} \\exp\\left(-\\frac{(x-\\mu)^2}{2\\sigma^2} \\right)\n",
+    "$$\n",
+    "\n",
+    "In the SLR model, the conditional distribution has * this * distribution. \n",
+    "\n",
+    "That is, for any single observation, $y_i$\n",
+    "$$\n",
+    "f(y_i|\\beta_0, \\beta_1, x_i) = \\frac{1}{\\sqrt{2\\sigma^2 \\pi}} \\exp\\left(-\\frac{(y_i-(\\beta_0+\\beta_1 x_i))^2}{2\\sigma^2} \\right)\n",
+    "$$\n",
+    "\n",
+    "Interpreting this function as a function of the parameters $\\theta=\\{ \\beta_0, \\beta_1, \\sigma \\}$, then it gives us the likelihood of the $i^{\\mathrm{th}}$ data point. \n",
+    "\n",
+    "As we did for the simple binomial distribution (see [lecture](https://github.com/vectorbite/VBiTraining2/tree/master/lectures)), we can use this to estimate the parameters of the model."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "We will use R. For starters, clear all variables and graphic devices and load necessary packages:"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 12,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "rm(list = ls())\n",
+    "graphics.off()"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Implementing the Likelihood in R\n",
+    "\n",
+    "First, we need to build an R function that returns the (negative log) likelihood for simple linear regression (it is negative log because the log of likelihood is itself negative):"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 1,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "nll.slr <- function(par, dat, ...){\n",
+    " args <- list(...)\n",
+    " \n",
+    " b0 <- par[1]\n",
+    " b1 <- par[2]\n",
+    " X <- dat$X\n",
+    " Y <- dat$Y\n",
+    " if(!is.na(args$sigma)){\n",
+    "  sigma <- args$sigma\n",
+    " } else \n",
+    "  sigma <- par[3]\n",
+    "\n",
+    " mu <- b0+b1 * X\n",
+    " \n",
+    " return(-sum(dnorm(Y, mean=mu, sd=sigma, log=TRUE)))\n",
+    "}"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "Note that we do something a bit different here (the \"`...`\" bit). We do it this way because we want to be able to use R's `optim()` function later.\n",
+    "\n",
+    "The `dnorm()` function calculates the logged (the `log=TRUE` argument) probability of observing Y given mu, sigma and that X. \n",
+    "\n",
+    "The negative sign on `sum()` is because the `optim()` function in R will minimize the negative log-likelihood, which is a sum: Recall that The log-likelihood of the parameters $\\theta$ being true given data x equals to the sum of the logged probability densities of observing the data x given parameters $\\theta$. We want to maximize this (log-) likelihood using `optim()`."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "Let's generate some simulated data, assuming that: $\\beta_0=$ `b0`, $\\beta_1=$ `b1`, and $\\sigma=$ `sigma`. For this, we will generate random deviations to simulate sampling or measurement error around an otherwise perfect line of data values:"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 2,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "set.seed(123)\n",
+    "n <- 30\n",
+    "b0 <- 10\n",
+    "b1 <- 3\n",
+    "sigma <- 2\n",
+    "X <- rnorm(n, mean=3, sd=7)\n",
+    "Y <- b0 + b1 * X + rnorm(n, mean=0, sd=sigma)\n",
+    "dat <- data.frame(X=X, Y=Y) # convert to a data frame"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "In the first line, we `set.seed()` to ensure that we can reproduce the results. The seed number you choose is the starting point used in the generation of a sequence of random numbers. No plot the \"data\":"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 3,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "image/png": 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G6kU99OvP3b/G3PVe8X45HcgpBwXOaT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\nAABJRU5ErkJggg==",
+      "text/plain": [
+       "plot without title"
+      ]
+     },
+     "metadata": {
+      "image/png": {
+       "height": 420,
+       "width": 420
+      }
+     },
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "plot(X, Y)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "### Likelihood profile\n",
+    "\n",
+    "For now, let's assume that we know what $\\beta_1$ is. Let's build a likelihood profile for the simulated data:"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 5,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "N <- 50\n",
+    "b0s <- seq(5, 15, length=N)\n",
+    "mynll <- rep(NA, length=50)\n",
+    "for(i in 1:N){\n",
+    " mynll[i] <- nll.slr(par=c(b0s[i],b1), dat=dat, sigma=sigma)\n",
+    "}"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "That is, we calculate the negative log-likelihood for fixed b1, across a range (5 - 15) of b0. "
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "Now plot the profile:"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 6,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "image/png": 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V9++UU6BAAACGPYKV6jRo0aNGiwevVq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\nAAAAAElFTkSuQmCC",
+      "text/plain": [
+       "plot without title"
+      ]
+     },
+     "metadata": {
+      "image/png": {
+       "height": 420,
+       "width": 420
+      }
+     },
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "plot(b0s, mynll, type=\"l\")\n",
+    "abline(v=b0, col=2)\n",
+    "abline(v=b0s[which.min(mynll)], col=3)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "The true value for b0 (10) is the red line, while the value that minimizes the log-likelihood (i.e., maximizes the negative log-likelihood) is the green line. These are not the same because maximum likelihood is providing an * estimate * of the true value given the measurement errors (that we ourselves generated in tgis synthetic dataset). "
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "(MLE-LikelihoodSurface)=\n",
+    "### Likelihood surface\n",
+    "\n",
+    "If we wanted to estimate both $\\beta_0$ and $\\beta_1$ (two parameters), we need to deal with a two-dimensional maximum likelihood surface. The simplest approach is to do a *grid search* to find this likelihood surface."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 7,
+   "metadata": {
+    "scrolled": true
+   },
+   "outputs": [
+    {
+     "data": {
+      "text/html": [
+       "<table>\n",
+       "<caption>A matrix: 2 × 2 of type dbl</caption>\n",
+       "<tbody>\n",
+       "\t<tr><td>10.00000</td><td>3.00</td></tr>\n",
+       "\t<tr><td>10.48485</td><td>2.96</td></tr>\n",
+       "</tbody>\n",
+       "</table>\n"
+      ],
+      "text/latex": [
+       "A matrix: 2 × 2 of type dbl\n",
+       "\\begin{tabular}{ll}\n",
+       "\t 10.00000 & 3.00\\\\\n",
+       "\t 10.48485 & 2.96\\\\\n",
+       "\\end{tabular}\n"
+      ],
+      "text/markdown": [
+       "\n",
+       "A matrix: 2 × 2 of type dbl\n",
+       "\n",
+       "| 10.00000 | 3.00 |\n",
+       "| 10.48485 | 2.96 |\n",
+       "\n"
+      ],
+      "text/plain": [
+       "     [,1]     [,2]\n",
+       "[1,] 10.00000 3.00\n",
+       "[2,] 10.48485 2.96"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    },
+    {
+     "data": {
+      "image/png": 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SA0QdjB2xxNSQ6BMA/9B/gbYQcfs7ca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\nrvQ7AAAAAElFTkSuQmCC",
+      "text/plain": [
+       "plot without title"
+      ]
+     },
+     "metadata": {
+      "image/png": {
+       "height": 420,
+       "width": 420
+      }
+     },
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "N0 <- 100\n",
+    "N1 <- 101\n",
+    "b0s <- seq(7,12, length=N0)\n",
+    "b1s <- seq(1,5, length=N1)\n",
+    "\n",
+    "mynll <- matrix(NA, nrow=N0, ncol=N1)\n",
+    "for(i in 1:N0){\n",
+    " for(j in 1:N1) mynll[i,j] <- nll.slr(par=c(b0s[i],b1s[j]), dat=dat, sigma=sigma)\n",
+    "}\n",
+    "\n",
+    "ww <- which(mynll==min(mynll), arr.ind=TRUE)\n",
+    "\n",
+    "b0.est <- b0s[ww[1]]\n",
+    "b1.est <- b1s[ww[2]]\n",
+    "rbind(c(b0, b1), c(b0.est, b1.est))\n",
+    "\n",
+    "filled.contour(x = b0s, y = b1s, z= mynll, col=heat.colors(21), \n",
+    "    plot.axes = {axis(1); axis(2); points(b0,b1, pch=21); \n",
+    "       points(b0.est, b1.est, pch=8, cex=1.5); xlab=\"b0\"; ylab=\"b1\"})"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "There is a lot going on here. Make sure you ask one of us if some of the code does not make sense!\n",
+    "\n",
+    "Again, note that the true parameter combination (asterisk) and the one what maximizes the negative log-likelihood (circle) are different."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "### Conditional Likelihood\n",
+    "We can also look at the conditional surfaces (i.e., we look at the slice around whatever the best estimate is for the other parameter):"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 60,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "image/png": 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Idujg8M9LgFaAR7YvuchMSumZn4KDDE4UIvYvV2nG3UEj+58kzEXEkYIe0GO+YT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\nxCJQILEIFEgsAgUSi0CBxCJQILEIFP4f9ydLw4j6XPQAAAAASUVORK5CYII=",
+      "text/plain": [
+       "plot without title"
+      ]
+     },
+     "metadata": {
+      "image/png": {
+       "height": 360,
+       "width": 300
+      }
+     },
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "par(mfrow=c(1,2), bty=\"n\")\n",
+    "plot(b0s, mynll[,ww[2]], type=\"l\", xlab=\"b0\", ylab=\"NLL\")\n",
+    "plot(b1s, mynll[ww[1],], type=\"l\", xlab=\"b1\", ylab=\"NLL\")"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Alternatives to Grid Search\n",
+    "\n",
+    "There are many alternative methods to grid searches. Since we are seeking to minimize an arbitrary function (the negative log likelihood) we typically use a descent method to perform general optimization.\n",
+    "\n",
+    "There are lots of options implemented in the `optim`function in R. We won't go into the details of these methods, due to time constraints. However, typically one would most commonly use:\n",
+    "\n",
+    " * Brent's method: for 1-D search within a bounding box, only\n",
+    " * L-BFGS-B (limited-memory Broyden–Fletcher–Goldfarb–Shanno algorithm with bounding box constraints): a quasi-Newton method, used for higher dimensions, when you want to be able to put simple limits on your search area. \n",
+    " \n",
+    "\n",
+    "## Maximum Likelihood using `optim()`\n",
+    "\n",
+    "We can now do the fitting. This involves optimization (to find the appropriate parameter values that achieve the maximum of the likelihood surface above). For this, we will use R's versatile `optim()` function.\n",
+    "\n",
+    "The first argument for `optim()` is the function that you want to minimize, and the second is a vector of starting values for your parameters (as always, do a`?optim`). After the main arguments, you can add what you need to evaluate your function (e.g. `sigma` ). The addtional argument sigma can be \"fed\" to `nll.slr` because we use the `...` convention when defining it."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 61,
+   "metadata": {
+    "scrolled": true
+   },
+   "outputs": [
+    {
+     "data": {
+      "text/html": [
+       "<dl>\n",
+       "\t<dt>$par</dt>\n",
+       "\t\t<dd><style>\n",
+       ".list-inline {list-style: none; margin:0; padding: 0}\n",
+       ".list-inline>li {display: inline-block}\n",
+       ".list-inline>li:not(:last-child)::after {content: \"\\00b7\"; padding: 0 .5ex}\n",
+       "</style>\n",
+       "<ol class=list-inline><li>10.4589351280817</li><li>2.96170447551098</li></ol>\n",
+       "</dd>\n",
+       "\t<dt>$value</dt>\n",
+       "\t\t<dd>58.2247252772924</dd>\n",
+       "\t<dt>$counts</dt>\n",
+       "\t\t<dd><style>\n",
+       ".dl-inline {width: auto; margin:0; padding: 0}\n",
+       ".dl-inline>dt, .dl-inline>dd {float: none; width: auto; display: inline-block}\n",
+       ".dl-inline>dt::after {content: \":\\0020\"; padding-right: .5ex}\n",
+       ".dl-inline>dt:not(:first-of-type) {padding-left: .5ex}\n",
+       "</style><dl class=dl-inline><dt>function</dt><dd>12</dd><dt>gradient</dt><dd>12</dd></dl>\n",
+       "</dd>\n",
+       "\t<dt>$convergence</dt>\n",
+       "\t\t<dd>0</dd>\n",
+       "\t<dt>$message</dt>\n",
+       "\t\t<dd>'CONVERGENCE: REL_REDUCTION_OF_F &lt;= FACTR*EPSMCH'</dd>\n",
+       "</dl>\n"
+      ],
+      "text/latex": [
+       "\\begin{description}\n",
+       "\\item[\\$par] \\begin{enumerate*}\n",
+       "\\item 10.4589351280817\n",
+       "\\item 2.96170447551098\n",
+       "\\end{enumerate*}\n",
+       "\n",
+       "\\item[\\$value] 58.2247252772924\n",
+       "\\item[\\$counts] \\begin{description*}\n",
+       "\\item[function] 12\n",
+       "\\item[gradient] 12\n",
+       "\\end{description*}\n",
+       "\n",
+       "\\item[\\$convergence] 0\n",
+       "\\item[\\$message] 'CONVERGENCE: REL\\_REDUCTION\\_OF\\_F <= FACTR*EPSMCH'\n",
+       "\\end{description}\n"
+      ],
+      "text/markdown": [
+       "$par\n",
+       ":   1. 10.4589351280817\n",
+       "2. 2.96170447551098\n",
+       "\n",
+       "\n",
+       "\n",
+       "$value\n",
+       ":   58.2247252772924\n",
+       "$counts\n",
+       ":   function\n",
+       ":   12gradient\n",
+       ":   12\n",
+       "\n",
+       "\n",
+       "$convergence\n",
+       ":   0\n",
+       "$message\n",
+       ":   'CONVERGENCE: REL_REDUCTION_OF_F &lt;= FACTR*EPSMCH'\n",
+       "\n",
+       "\n"
+      ],
+      "text/plain": [
+       "$par\n",
+       "[1] 10.458935  2.961704\n",
+       "\n",
+       "$value\n",
+       "[1] 58.22473\n",
+       "\n",
+       "$counts\n",
+       "function gradient \n",
+       "      12       12 \n",
+       "\n",
+       "$convergence\n",
+       "[1] 0\n",
+       "\n",
+       "$message\n",
+       "[1] \"CONVERGENCE: REL_REDUCTION_OF_F <= FACTR*EPSMCH\"\n"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "fit <- optim(nll.slr, par=c(2, 1), method=\"L-BFGS-B\", ## this is a n-D method\n",
+    "    lower=-Inf, upper=Inf, dat=dat, sigma=sigma)\n",
+    "\n",
+    "fit"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "Easy as pie (once you have the recipe)! We can also fit sigma as the same time if we want:"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 62,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/html": [
+       "<style>\n",
+       ".list-inline {list-style: none; margin:0; padding: 0}\n",
+       ".list-inline>li {display: inline-block}\n",
+       ".list-inline>li:not(:last-child)::after {content: \"\\00b7\"; padding: 0 .5ex}\n",
+       "</style>\n",
+       "<ol class=list-inline><li>10.4589449542964</li><li>2.96170371229526</li><li>1.62168936031414</li></ol>\n"
+      ],
+      "text/latex": [
+       "\\begin{enumerate*}\n",
+       "\\item 10.4589449542964\n",
+       "\\item 2.96170371229526\n",
+       "\\item 1.62168936031414\n",
+       "\\end{enumerate*}\n"
+      ],
+      "text/markdown": [
+       "1. 10.4589449542964\n",
+       "2. 2.96170371229526\n",
+       "3. 1.62168936031414\n",
+       "\n",
+       "\n"
+      ],
+      "text/plain": [
+       "[1] 10.458945  2.961704  1.621689"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "fit <- optim(nll.slr, par=c(2, 1, 5), method=\"L-BFGS-B\", ## this is a n-D method\n",
+    "    lower=c(-Inf, -Inf, 0.1), upper=Inf, dat=dat, sigma=NA)\n",
+    "fit$par"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "The starting values (b0 = 2, b1 = 1, sigma = 5) need to be assigned as we would do for NLLS. Also note that much like NLLS, we have bounded the parameters. The exact starting values are not too important in this case (try changing them see what happens)."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "Now visualize the fit:"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 63,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "image/png": 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ebOg7zPN7FaLSMUyuYHWbZtwXVMc4Yi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\nlr8lh+QAAAAASUVORK5CYII=",
+      "text/plain": [
+       "plot without title"
+      ]
+     },
+     "metadata": {
+      "image/png": {
+       "height": 360,
+       "width": 300
+      }
+     },
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "plot(X, Y)\n",
+    "abline(a=fit$par[1], b=fit$par[2], col=2, lwd=2)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "### Confidence intervals\n",
+    "\n",
+    "The joint distribution of the MLEs are asymptotically Normally distributed. Given this, if you are minimizing the negative log likelihood (NLL) then the covariance matrix of the estimates is (asymptotically) the inverse of the Hessian matrix. The Hessian matrix evalutes the second derivatives of the NLL (numerically here), which gives us information about the curvature the likelihood. Thus we can use the Hessian to estimate confidence intervals:"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 64,
+   "metadata": {
+    "scrolled": true
+   },
+   "outputs": [
+    {
+     "data": {
+      "text/html": [
+       "<table>\n",
+       "<caption>A data.frame: 2 × 3</caption>\n",
+       "<thead>\n",
+       "\t<tr><th scope=col>value</th><th scope=col>upper</th><th scope=col>lower</th></tr>\n",
+       "\t<tr><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th></tr>\n",
+       "</thead>\n",
+       "<tbody>\n",
+       "\t<tr><td>10.458935</td><td>11.228565</td><td>9.689305</td></tr>\n",
+       "\t<tr><td> 2.961704</td><td> 3.067705</td><td>2.855704</td></tr>\n",
+       "</tbody>\n",
+       "</table>\n"
+      ],
+      "text/latex": [
+       "A data.frame: 2 × 3\n",
+       "\\begin{tabular}{lll}\n",
+       " value & upper & lower\\\\\n",
+       " <dbl> & <dbl> & <dbl>\\\\\n",
+       "\\hline\n",
+       "\t 10.458935 & 11.228565 & 9.689305\\\\\n",
+       "\t  2.961704 &  3.067705 & 2.855704\\\\\n",
+       "\\end{tabular}\n"
+      ],
+      "text/markdown": [
+       "\n",
+       "A data.frame: 2 × 3\n",
+       "\n",
+       "| value &lt;dbl&gt; | upper &lt;dbl&gt; | lower &lt;dbl&gt; |\n",
+       "|---|---|---|\n",
+       "| 10.458935 | 11.228565 | 9.689305 |\n",
+       "|  2.961704 |  3.067705 | 2.855704 |\n",
+       "\n"
+      ],
+      "text/plain": [
+       "  value     upper     lower   \n",
+       "1 10.458935 11.228565 9.689305\n",
+       "2  2.961704  3.067705 2.855704"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "fit <- optim(nll.slr, par=c(2, 1), method=\"L-BFGS-B\", hessian=TRUE, lower=-Inf, upper=Inf, dat=dat, sigma=sigma)\n",
+    "\n",
+    "fisher_info <- solve(fit$hessian)\n",
+    "est_sigma <- sqrt(diag(fisher_info))\n",
+    "upper <- fit$par+1.96 * est_sigma\n",
+    "lower <- fit$par-1.96 * est_sigma\n",
+    "interval <- data.frame(value=fit$par, upper=upper, lower=lower)\n",
+    "interval"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "### Comparison to fitting with least squares\n",
+    "\n",
+    "We can, of course, simply fit the model with lest squares using the `lm()` function:"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 65,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/html": [
+       "<table>\n",
+       "<caption>A matrix: 2 × 4 of type dbl</caption>\n",
+       "<thead>\n",
+       "\t<tr><th></th><th scope=col>Estimate</th><th scope=col>Std. Error</th><th scope=col>t value</th><th scope=col>Pr(&gt;|t|)</th></tr>\n",
+       "</thead>\n",
+       "<tbody>\n",
+       "\t<tr><th scope=row>(Intercept)</th><td>10.458936</td><td>0.32957007</td><td>31.73509</td><td>1.699822e-23</td></tr>\n",
+       "\t<tr><th scope=row>X</th><td> 2.961704</td><td>0.04539126</td><td>65.24834</td><td>3.874555e-32</td></tr>\n",
+       "</tbody>\n",
+       "</table>\n"
+      ],
+      "text/latex": [
+       "A matrix: 2 × 4 of type dbl\n",
+       "\\begin{tabular}{r|llll}\n",
+       "  & Estimate & Std. Error & t value & Pr(>\\textbar{}t\\textbar{})\\\\\n",
+       "\\hline\n",
+       "\t(Intercept) & 10.458936 & 0.32957007 & 31.73509 & 1.699822e-23\\\\\n",
+       "\tX &  2.961704 & 0.04539126 & 65.24834 & 3.874555e-32\\\\\n",
+       "\\end{tabular}\n"
+      ],
+      "text/markdown": [
+       "\n",
+       "A matrix: 2 × 4 of type dbl\n",
+       "\n",
+       "| <!--/--> | Estimate | Std. Error | t value | Pr(&gt;|t|) |\n",
+       "|---|---|---|---|---|\n",
+       "| (Intercept) | 10.458936 | 0.32957007 | 31.73509 | 1.699822e-23 |\n",
+       "| X |  2.961704 | 0.04539126 | 65.24834 | 3.874555e-32 |\n",
+       "\n"
+      ],
+      "text/plain": [
+       "            Estimate  Std. Error t value  Pr(>|t|)    \n",
+       "(Intercept) 10.458936 0.32957007 31.73509 1.699822e-23\n",
+       "X            2.961704 0.04539126 65.24834 3.874555e-32"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "lmfit <- lm(Y~X)\n",
+    "\n",
+    "summary(lmfit)$coeff"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "The estimates we get using `optim()` are almost identical to the estimates that we obtain here, and the standard errors on the intercept and slope are very similar to those we calculated from the Hessian (est_sigma= `r est_sigma`). "
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Model Selection\n",
+    "\n",
+    "You can use [AIC or BIC as you did in NLLS](#Comparing-models) using the likelihood you have calculated. \n",
+    "\n",
+    "You can also use the Likelihood Ratio Test (LRT).\n",
+    "\n",
+    "## Exercises <a id='MLE_Exercises'></a> \n",
+    "\n",
+    "Try MLE fitting for the allometric trait data example [above](#Allometric-scaling-of-traits). You will use the same data + functions that you used to practice fitting curves using non-linear least squares methods. You have two options here. The easier one is to convert the power law model to a straight line model by taking a log (explained the Allometry [Exercises](#Allom_Exercises). Specifically,\n",
+    "\n",
+    "(a) Using the [`nll.slr`](#Implementing-the-Likelihood-in-R) function as an example, write a function that calculates the negative log likelihood as a function of the parameters describing your trait and any additional parameters you need for an appropriate noise distribution (e.g., $\\sigma$ if you have normally distributed errors).\n",
+    "\n",
+    "(b) For at least one of your parameters plot a likelihood profile given your data, with the other parametes fixed.\n",
+    "\n",
+    "(c) Use the `optim` function to find the MLE of the same parameter and indicate this on your likelihood profile.\n",
+    "\n",
+    "(d) Obtain a confidence interval for your estimate.\n",
+    "\n",
+    "A more challenging option is to fit the allometry data directly to the power law equation. You would need to assume a log-normal distribution for the errors instead of normal, in this case. "
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "# Readings and Resources <a id='Readings-MLE'></a>\n",
+    "\n",
+    " * Bolker, B. Ecological models and data in R. (Princeton University Press, 2008). "
+   ]
+  }
+ ],
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