{ "cells": [ { "cell_type": "markdown", "id": "d90e2ec2-a2ad-411e-a9b3-0042f83ccb46", "metadata": {}, "source": [ "# The Subject of Probability\n", "\n", "Probability is the basis for statistics and an intricate tool used for dealing with what we call non-deterministic events; that is, we do not know the outcome of an event before it occurs. Most of mathematics deals with deterministic events, e.g. \"If I have 5 coins and you take 1 away, I have 4 coins left.\" Probability does not work the same way since I can flip a coin several times and each flip can come out differently. It is often described as \"being up to chance\" what the outcome will be even though chance is not an actor that can be responsible for anything. What is responsible for different results? We do not know. In events where not everything is known, we rely on probability to help us understand what can happen. Because of this, it is essential to be certain of one's interpretation of probability, especially when looking to make decisions.\n", "\n", "We all think that we understand probability, but as mentioned before probability is an intricate tool. Take special care with the definitions provided in this chapter. Probability is not an intuitive subject. Random improbable events happen, and yet we are surprised when they happen to us. The exclamation \"Impossible! There was only a 1% chance of that happening!\" contradicts itself. The one-percent chance is a very real chance. In our minds, we have some belief about how probable an event is to happen and often we say a 1% chance is not enough to consider a valid possibility and we discard it. Perhaps for small stakes this is acceptable, but in other cases the 1% chance of a large loss may need to be considered. In fact, if the experiment where the undesirable outcome can happen is performed 1000 times, it would be more surprising *not* to see this outcome at least once.\n", "\n", "This chapter explains how use probability as a tool instead of as a reason to dismiss the improbable.\n", "\n", "## What is a Probability?\n", "\n", "First, let us define a probability (or a chance as is often used) as \"the expected frequency with which a certain outcome is observed when an experiment is repeated indefinitely.\" This tells us a couple things about a probability. Its value is always between 0 and 1, and its \"true\" value can never be observed since we cannot infinitely flip a coin or repeat any other sort of experiment. However, because it is an *expected* frequency, we do not need to know the \"true\" value of a probability to make use of it. \n", "\n", "Another detail we must specify is whether this experiment has been performed already or not. In this course, we will approach problem from a subjectivist's perspective where anything unknown can be assigned a probability. This is opposed to a frequentist's perspective which is only concerned with the true state of the world. Say a teacher tosses a coin, catches it, and asks a student the probability of it being heads. Most people would say 50 percent without even thinking. They are saying that they expect the coin to be heads just as much as they expect it to be tails. A frequentist would say, \"You have already tossed the coin. Probability is not appropriate in this situation.\" This course is not designed for that inflexible kind of thinking. Instead, we will use the subjectivist perspective since that is more similar to the way we already think of probability." ] }, { "cell_type": "markdown", "id": "6ec060f3-3706-406f-a020-ad682a1f73dc", "metadata": {}, "source": [ "## Probability Terms" ] }, { "cell_type": "markdown", "id": "470e9c10-7e32-4f2b-8f51-736a515cc020", "metadata": {}, "source": [ "TODO: I need to find a way to use these in a narrative to illustrate them.\n", "* sample space - the set of all possible outcomes and events from an experiment; also, the set of values (or domain) that a random variable can take on\n", "* experiment - a situation with one or more outcomes; remember, in our interpretations the experiment can already have run to completion without us having observed an outcome\n", "* random variable (rv) - a component in an experiment that takes on a value\n", "* outcome - the state of our random variable at the end of an experiment, whether observed or not\n", "* state - a deterministic value for a variable\n", "* event - a set of outcomes for an experiment; e.g. $A$ can be defined as rolling a pair of dice and obtaining an even number" ] }, { "cell_type": "markdown", "id": "fdd71432-93aa-4824-a7bf-6edffa639aa7", "metadata": {}, "source": [ "## Random Variables" ] }, { "cell_type": "markdown", "id": "1988d3d8-fe92-4621-95be-b5cde3845844", "metadata": {}, "source": [ "Random variables are one of the building blocks of probability. Instead of blaming chance, we define a random variable which encapsulates all of the unknowns influencing a particular value in our experiment. The value of this random variable will change from experiment to experiment (if we have multiple experiments).\n", "\n", "Mathematically, rvs have certain properties.\n", "\n", "1. rvs can either be discrete or continuous. Discrete means they can only take on certain values, often nonnegative whole numbers. Continuous means they can take on any value within a certain range such as $(-\\infty, \\infty)$ or $[0, \\infty)$ or $[0,1]$.\n", "\n", "2. Discrete rvs have a pmf or probability mass function which gives the relative probability/frequency of them taking on a value and it is written as $P(X=k) = f_X(k)$. Continuous rvs had a pdf or probability density function which also gives the relative probability/frequency of them taking on a specific value. It is written as $P(x" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "plt.figure(figsize=(10,8))\n", "plt.bar(np.arange(0,12), binom.pmf(np.arange(0,12), 11, .5))\n", "plt.title(\"Probability Mass Function of a Binomial RV (Discrete)\", fontsize=16)\n", "plt.ylabel(\"Probability\", fontsize=16)\n", "plt.xlabel(\"Value of Binomial RV\", fontsize=16)\n", "plt.xticks(np.arange(0,12))\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 7, "id": "c7ed66a7-5442-489a-9570-8157f61d8e8f", "metadata": {}, "outputs": [ { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "plt.figure(figsize=(10,8))\n", "plt.plot(np.linspace(0.,12,100), norm.pdf(np.linspace(0.,11.,100), 5.5, 5.5/3.))\n", "plt.title(\"Probability Density Function of a Normal RV (Continuous)\", fontsize=16)\n", "plt.ylabel(\"Probability\", fontsize=16)\n", "plt.xlabel(\"Value of Normal RV\", fontsize=16)\n", "plt.xticks(np.arange(0,13))\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 8, "id": "18ced9ad-dce7-464a-a2c5-78dca462227e", "metadata": {}, "outputs": [ { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "plt.figure(figsize=(10,8))\n", "plt.plot(np.linspace(0.,12.,100), norm.cdf(np.linspace(0.,12.,100), 5.5, 5.5/3.))\n", "plt.title(\"Cumulative Distribution Function of a Normal RV\", fontsize=16)\n", "plt.ylabel(\"Probability\", fontsize=16)\n", "plt.xlabel(\"Value of Normal RV\", fontsize=16)\n", "plt.xticks(np.arange(0,13))\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "8d8a554f-a8f9-4a66-8bb6-5dbf80d64ad3", "metadata": {}, "source": [ "3. Discrete rvs can have distributions (pmf's) with irregular intervals between possible values, and continuous rvs can have distributions (pdf's) that are not differentiable. Essentially, whatever distribution you can conceive, a rv can have. This allows rv's to represent something as flexible as human beliefs.\n", "\n", "4. There are many predefined discrete and continuous probability distrbutions. Above are shown examples of binomial and gaussian/normal distributions. Often, probability distributions are suited to specific kinds of events. For instance, a binomial distribution represents the probability of observing a certain number of successes $k$ in an experiment with $n$ trials where each trial has a probability of success $p$. Thus if $X$ is a rv that has a binomial distribution, then the probability that $X$ is equal to any value $k$ can be written as pmf $f_X(k; n, p) = {n \\choose k} \\cdot k^p \\cdot (n-k)^{1-p}$.\n", "\n", " The normal distribution is less interpretable but is often used to represent a variable that has an equal chance of being above or below its expected value by a certain distance. Just as the pmf of a binomial distribution is parametrized by $n$ and $p$, a normal distribution is parametrized by $\\mu$ and $\\sigma$ where $\\mu$ is the expected value of the variable and $\\sigma$ is proportional to the distance observed above or below the mean. A rv $Y$ that is normally distributed has a pdf $f_Y(y; \\mu, \\sigma^2) = \\frac{1}{\\sigma\\sqrt{2\\pi}} \\cdot \\exp\\left({\\frac{(y-\\mu)^2}{2\\sigma^2}}\\right)$\n", " \n", " rvs with a parametrized distribution like this are often defined in the following manner. A binomial rv $X$ is defined by $X \\sim \\text{Binom}(n, p)$ and a normal rv $Y$ is defined by $Y \\sim N(\\mu, \\sigma^2)$. The two variables shown are $X \\sim \\text{Binom}(11,.5)$ and $Y \\sim N\\left(5.5, \\left(\\frac{5.5}{3}\\right)^2\\right)$. And remember these are just two distributions [out of many][1].\n", " \n", "[1]: https://en.wikipedia.org/wiki/List_of_probability_distributions\n", " \n", "5. Probability distributions can also be described in other ways. For example, numeric random variables all have expected values and variances, written as $E(X)$ and $\\text{Var}(X)$. The expected value can also be called the mean, or the average of all the values we would see if we conducted a large number of experiments. The variance is representative of how spread out the values between experiments should be. The square root of the variance is what we call standard deviation and is another measure for how much a random variable can vary. There are also other metrics such as skewness and kurtosis which we will not touch on in this course as they have little relevance, nor will we discuss how to calculate any values other than expected value. It suffices to know how to find a mean and that as variance (or standard deviation) increases, so will the distance between observations." ] }, { "cell_type": "markdown", "id": "ec016092-39a2-4e88-95d1-11f6e17bb1e1", "metadata": {}, "source": [ "## Joint, Marginal, and Conditional Probability\n", "\n", "The last essential concept we need to know about probability is how random variables interact with each other. This where we define joint, marginal, and conditional probability. Up until now, we have only considered using a single random variable at a time. Each random variable has a 1-dimensional domain or sample space. Both $X$ and $Y$ previously have 1 value they can take on at a time. For $X$ the domain is $[0,1,2,3,4,5,6,7,8,9,10,11]$. For $Y$ it is all real numbers $(-\\infty, \\infty)$. Because they are 1-dimensional we can graph them on the x-axis and the pmf, pdf, or cdf on the y-axis as shown.\n", "\n", "If we like, we can also visualize the probability of two variables taking on a specific set of values.\n", "Let's say we have two independent random variables $A$ and $B$ which both have a standard normal distribution (that is, $N(0,1)$).\n", "Their probability density *together* at any point in 2-dimensional space would look like this:" ] }, { "cell_type": "code", "execution_count": 80, "id": "448d569e-be31-4e22-9a8e-138679ef9b05", "metadata": {}, "outputs": [ { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "from matplotlib import cm\n", "from matplotlib.ticker import LinearLocator\n", "\n", "fig, ax = plt.subplots(subplot_kw={\"projection\": \"3d\"}, figsize=(14,10))\n", "\n", "# Make data.\n", "x = np.linspace(-3.5, 3.5, 100)\n", "y = np.linspace(-3.5, 3.5, 100)\n", "X, Y = np.meshgrid(x, y)\n", "\n", "line = norm.pdf(x) * norm.pdf(-.9)\n", "\n", "Z = norm.pdf(X) * norm.pdf(Y)\n", "\n", "# Plot the surface.\n", "surf = ax.plot_surface(X, Y, Z, cmap=cm.coolwarm,\n", " linewidth=0, antialiased=False)\n", "ax.plot(x, np.full(100,-1.3), line, 'go', alpha=.5)\n", "\n", "# Customize the z axis.\n", "ax.set_zlim(0, .15)\n", "ax.zaxis.set_major_locator(LinearLocator(10))\n", "# A StrMethodFormatter is used automatically\n", "ax.zaxis.set_major_formatter('{x:.02f}')\n", "\n", "# Add a color bar which maps values to colors.\n", "fig.colorbar(surf, shrink=0.5, aspect=5)\n", "\n", "ax.set_xlabel('A', fontsize=14)\n", "ax.set_ylabel('B', fontsize=14)\n", "ax.set_zlabel('Probability Density', fontsize=14)\n", "plt.title('Joint Probability Density of Two Normal Random Variables', fontsize=16)\n", "\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": null, "id": "43e05c3e-3e8b-4b5e-af0d-361f433e50ba", "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "markdown", "id": "e12210a7-bda2-4568-b338-fa9eeb0d5061", "metadata": {}, "source": [ "### Independent Variables" ] }, { "cell_type": "markdown", "id": "61cb81e6-9885-4413-9d53-8fec556e5a9b", "metadata": {}, "source": [ "## Bayes' Rule" ] }, { "cell_type": "markdown", "id": "c936a84d-6aba-4a23-8770-19303896d827", "metadata": {}, "source": [ "* Joint probability (marginal probability, conditional probability)\n", "* Independent variables\n", "* Properties of pmf's and pdf's\n", " * Expected value/mean\n", " * Variance/standard deviation\n", "* Different probability distributions\n", "* Bayes' Rule" ] }, { "cell_type": "code", "execution_count": null, "id": "1242a7a3-0d42-4b87-81db-e5228b9f0cb1", "metadata": {}, "outputs": [], "source": [] } ], "metadata": { "kernelspec": { "display_name": "Python 3 (ipykernel)", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.8.10" } }, "nbformat": 4, "nbformat_minor": 5 }