{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "I've recently been hit by something I would describe as \"being bit by the bayesian bug\".\n", "\n", "Things got started when my friend Anders sent me a text with this timely \"math riddle\":\n", "\n", "> A serological test has 95% probability of returning **positive** for someone who has COVID-19 antibodies and 95% probability of returning **negative** for someone who has no COVID-19 antibodies.\n", ">\n", "> You get tested. The test returns **positive**. What is the probability that you have COVID-19 antibodies?\n", "\n", "DISCLAIMER: I have no idea if these numbers are accurate (but you can find more info on serology tests from the CDC [here](https://www.cdc.gov/coronavirus/2019-ncov/lab/serology-testing.html)).\n", "\n", "I knew at first sight that this is a classic question in statistics, and that it can be solved by applying [Bayes's theorem](https://en.wikipedia.org/wiki/Bayes%27_theorem). However, I lacked the skill to do it in practice. I decided to learn enough to be able this sort of question in the future. And it started a sort of Bayes' frenzy in my life." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Solving the Corona testing quizz " ] }, { "attachments": { "3blue1brown%20bayes.png": { "image/png": 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" } }, "cell_type": "markdown", "metadata": {}, "source": [ "I turned to YouTube to get a footing on what it takes to answer the above question (I also visited Wikipedia, but I didn't find the introductory stuff I was looking for there). And I found what I believe is a beautiful introduction to the subject in [3blue1brown's video about Bayes theorem](https://www.youtube.com/watch?v=HZGCoVF3YvM). \n", "\n", "The video asks this question and then shows how to answer it:\n", "\n", "> Steve is very shy and withdrawn, invariably helpful but with little interest in people or in the world of reality. A meek and tidy soul, he has a need for order and structure, and a passion for detail. What is more likely: Steve is a librarian or Steve is a farmer?\n", "\n", "I highly recommend the video. It introduces a drawing type which is useful and relevant for thinking about the above questions and has allowed me, as advertised by the video, to memorize Bayes's theorem for later use. \n", "\n", "Here's a screenshot from the video to give you an impression:\n", "\n", "![3blue1brown%20bayes.png](attachment:3blue1brown%20bayes.png)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "To come back to the intro question, we need to apply Bayes's theorem:\n", "\n", "$$\n", "P(H|E) = \\frac{P(E|H) P(H)}{P(E)}\n", "$$\n", "\n", "In the formula, the hypothesis *H* is \"I have COVID-19 antibodies\". The Evidence *E* is \"My test is positive\".\n", "P(E|H) is the likelihood my test is positive when I have COVID-19 antibodies, which is 95%. P(E) is the total probability of having a positive test. P(H) is the prior probability of having COVID-19 antibodies.\n", "\n", "The crucial part in applying the formula above lies in the data that is missing from the problem definition, P(H).\n", "P(H) is the general proportion of the population that has had COVID-19. In France, at the time of writing, there had been 160,000 confirmed cases (source: [Our World In Data](https://ourworldindata.org/coronavirus/country/france?country=~FRA)).\n", "This would bring the ratio of cases to total population to:" ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "0.24 %\n" ] } ], "source": [ "print(f\"{160000 / 67000000 * 100:.2f} %\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "However, this is not the true incidence in the population, it is only the confirmed incidence. To get closer to reality (I think...), I multiply this by ten to account for the fact that confirmed cases are less than total cases, getting an order of magnitude of 2.4 %. \n", "\n", "Pluggin this in the formula, I can now compute the answer to the question:" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "probability of having COVID-19 antibodies given a positive test: 31.8%.\n" ] } ], "source": [ "prior = 2.4 / 100.\n", "likelihood = 95 / 100.\n", "total_prob = prior * likelihood + (1 - prior) * 5 / 100.\n", "posterior = prior * likelihood / total_prob\n", "\n", "print(f\"probability of having COVID-19 antibodies given a positive test: {posterior * 100:.1f}%.\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Surprise, surprise, the chance of having antibodies is only 31.8%." ] }, { "attachments": { "bayes_corona.png": { "image/png": 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" } }, "cell_type": "markdown", "metadata": {}, "source": [ "To get a better intuitive understanding, I put the data in the interactive Bayes's theorem tool (https://www.skobelevs.ie/BayesTheorem/) that was linked to by 3blue1brown (I had to round them up since the tool only accepts integers):\n", "\n", "![bayes_corona.png](attachment:bayes_corona.png)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In the above diagram, we have:\n", "\n", "> H(ypothesis): I have antibodies\n", ">\n", ">not H: I don't have antibodies\n", ">\n", ">E(vidence): my test is positive\n", ">\n", ">(\"|\" is read as \"given\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Admittedly, I expected the probability to be much higher than 31.8%: I wrote to my friend who sent me the riddle I believed it to be 90%! \n", "\n", "But it makes intuitive sense when looking at the drawing: there are two kind of positive tests. The blue ones are the true positives and the green ones are the false positives. And since most people haven't been exposed to COVID-19, there are more false positives. Which in turn means that if you only know about the test (and assuming that you had no other symptoms), it is more likely than not that you don't have antibodies.\n", "\n", "Of course, this result *should not be taken too seriously*, since this is not the actual sensivity and specificity of current serological tests. But it illustrates the fact that a test with high perceived reliability is not in itself a guarantee for accuracy (something that apparently two thirds of doctors also fail to recognize according to [this article from Statistics Done Wrong](https://www.statisticsdonewrong.com/p-value.html#the-base-rate-fallacy-in-medical-testing))." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# XKCD " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Going down the path of Bayes's theorem, I have now realized what so many people have before me: you can spot lots of situations in real life where it applies. \n", "\n", "There's even an [obligatory XKCD](https://xkcd.com/2236/) about this:" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "![xkcd 2236](https://imgs.xkcd.com/comics/is_it_christmas.png)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "You might wonder what makes this comic interesting or connected to Bayes's theorem. I'll try to rephrase it. When we see a 99.73% accuracy, we are usually led to believe something works really well. That is not necessarily true and is particularly false in this case. \n", "\n", "Where does the 99.73% accuracy come from? Supposing the service always says no (and this is where the humour is), it will be correct 364 out of 365 days every year. What accuracy would that give?" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "99.73%\n" ] } ], "source": [ "print(f\"{364/365 * 100:.2f}%\")" ] }, { "attachments": { "bayes_xkcd.png": { "image/png": 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" } }, "cell_type": "markdown", "metadata": {}, "source": [ "Let's say that we are interested in the probability that it is Christmas given that the accuracy of the indication is 99.73%. That also means that it gives incorrect information at a rate of 0.27%. Plugging in these numbers in the interactive calculator, the diagram that represents this situation is (rounded to integers):\n", "\n", "![bayes_xkcd.png](attachment:bayes_xkcd.png)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "With:\n", "\n", "> H(ypothesis): it is Christmas\n", ">\n", "> not H: it is not Christmas\n", ">\n", "> p(correct evidence|H) = 99%\n", "> p(incorrect evidence|not H) = 1%" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Surprisingly, even with this high accuracy, there is only a 51% chance that it is really Christmas.\n", "\n", "We can conclude that for very rare events, an accuracy as high as 99.73% does not mean it *works*. \n", "\n", "In that case, applying Bayes's theorem tells us that this information is not useful enough to predict it is Christmas (see also the discussion at [explainxkcd](https://www.explainxkcd.com/wiki/index.php/2236))." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Allen Downey's book *Think Bayes* and the audience problem " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Since I'm now quite interested in the topic, I invested some time in the first chapters of [Think Bayes](https://greenteapress.com/wp/think-bayes/), a *free* book by Allen Downey. It introduces all the necessary tools to solve problems using the Bayesian framework (in Python). The included exercises are well worth studying. To give you a feeling for what the exercices are like, I'll solve one of those from Chapter 4, which made me scratch my head but is quite fun." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## The audience problem " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "For lack of a better name, I'll call it the *audience problem*." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "> Suppose you are giving a talk in a large lecture hall and you want to estimate the number of people in the audience. There are too many to count, so you ask how many people were born on May 11 and two people raise their hands. You ask how many were born on May 23 and 1 person raises their hand. Finally, you ask how many were born on August 1, and no one raises their hand.\n", ">\n", ">How many people are in the audience? What is the 90% credible interval for your estimate? \n", ">\n", ">Hint: Remember the binomial distribution.\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Writing this in terms of probabilities, we are looking for maximum value of $P(N|2B\\textrm{ and }1B\\textrm{ and }0B)$, where 2B means \"we know 2 people in the room have a birthday on a particular day\" (and so on for 1B and 0B), while $N$ is the size of the room.\n", "\n", "Applying Bayes's theorem, this transforms into:\n", "\n", "$$\n", "P(N|2B\\textrm{ and }1B\\textrm{ and }0B) = \\frac{ P(2B\\textrm{ and }1B\\textrm{ and }0B|N) P(N) }{ P(2B\\textrm{ and }1B\\textrm{ and }0B) }\n", "$$\n", "\n", "To answer this, we will break it down in two parts. \n", "\n", "First, what is $P(kB|N)$? \n", "\n", "Once we have that, we will use that to compute the answer to the problem." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Birthdays and the binomial " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Given a room full of $N$ people, what is the likelihood that there are $k$ people having a birthday on a particular day in the room, which we will write $P(kB|N)$ ? Although related, this is not the [Birthday paradox](https://en.wikipedia.org/wiki/Birthday_problem).\n", "\n", "The *hint* points us to an analogy between this problem and *biased* coin flips. For a given date, for each person, there is a 1/365 chance to be born on a chosen date and 364/365 chances to be born on a different date. Of course, this is not completely true. [Wikipedia says this](https://en.m.wikipedia.org/wiki/Birthday#Distribution_through_the_year):\n", "\n", "> According to a public database of births, birthdays in the United States are quite evenly distributed for the most part, but there tend to be more births in September and October.\n", "\n", "Still, we can now use the binomial distribution to model the likelihood of seeing $k$ people out of a group of $N$ being born on a particular day. So we can answer our first subproblem:\n", "\n", "$$\n", "P(kB|N) = \\binom {N}{k}\\left(\\frac{1}{365}\\right)^{k}\\left(\\frac{364}{365}\\right)^{N-k}\n", "$$\n", "\n", "\n", "\n", "Let's print out some examples:" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "probability of having 2 same birthdays in a group of 10 people: 0.0003304417689522596\n", "probability of having 2 same birthdays in a group of 100 people: 0.028395815838883412\n", "probability of having 2 same birthdays in a group of 1000 people: 0.24257828306055526\n", "probability of having 2 same birthdays in a group of 5000 people: 0.00010404383244978144\n", "\n", "probability of having 3 same birthdays in a group of 10 people: 2.420818820163081e-06\n", "probability of having 3 same birthdays in a group of 100 people: 0.002548342447079194\n", "probability of having 3 same birthdays in a group of 1000 people: 0.22169700228458852\n", "probability of having 3 same birthdays in a group of 5000 people: 0.0004762006177452762\n" ] } ], "source": [ "import numpy as np\n", "from scipy.stats import binom\n", "import matplotlib.pyplot as plt\n", "plt.style.use('bmh')\n", "\n", "def likelihood(simultaneous_birthdays, n_people):\n", " return binom.pmf(simultaneous_birthdays, n_people, 1/365)\n", "\n", "for n_people in [10, 100, 1000, 5000]:\n", " print(f\"probability of having 2 same birthdays in a group of {n_people} people: {likelihood(2, n_people)}\")\n", "\n", "print()\n", "\n", "for n_people in [10, 100, 1000, 5000]:\n", " print(f\"probability of having 3 same birthdays in a group of {n_people} people: {likelihood(3, n_people)}\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "An interesting thing showing up in these numerical values is that for 2 birthdays occuring on the same date, the probability rises and then goes down again. This can be understood by graphing the probability of seeing $k$ people sharing a birthday for a group of 10000 people:" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "k = np.arange(0, 10001)\n", "probs = likelihood(k, 10000)\n", "\n", "fig, (ax1, ax2)= plt.subplots(nrows=2)\n", "ax1.plot(k, probs)\n", "ax2.plot(k, probs)\n", "ax2.set_xlim(0, 100)\n", "for ax in [ax1, ax2]:\n", " ax.set_xlabel('k')\n", " ax.set_ylabel('probability')\n", " \n", "ax2.set_title('zoomed plot')\n", "plt.tight_layout()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "It appears that the number of birthdays is most probable for the expected value of $1/365 \\times N$. \n", "\n", "Hence, when increasing the number of people in the room from 10 to 5000, we pass this \"bump\" in the process which leads to an increase and then a decrease in probability." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Solution to the audience problem " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now on to the solution of the problem. \n", "We can further simplify the problem by applying the rule for independant events.\n", "$$\n", "P(N|2B\\textrm{ and }1B\\textrm{ and }0B) = \\frac{ P(2B\\textrm{ and }1B\\textrm{ and }0B|N) P(N) }{ P(2B\\textrm{ and }1B\\textrm{ and }0B) } = \\frac{ P(2B | N) P(1B|N) P(0B|N) P(N) }{ P(2B) P(1B) P(0B) }\n", "$$\n", "\n", "To compute this formula, we will set up a world of all possible room sizes $N$ called `hypos` and then apply the likelihood to each world separately." ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "1999" ] }, "execution_count": 6, "metadata": {}, "output_type": "execute_result" } ], "source": [ "from empiricaldist import Pmf\n", "\n", "hypos = np.arange(1, 2000) # let's say there are at maximum 2000 people in the room\n", "\n", "pmf = Pmf(1, hypos) # each hypothesis/world has the same probability at first (hence the 1)\n", "\n", "pmf.normalize() # normalize the probability distribution" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can now write the update function that allows us to process new evidence, of which we have three (2 people born on the same day, 1 on the same day, 0 on the same day). It makes use of the `likelihood` function that we wrote above for the computation of $P(kB|N)$." ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [], "source": [ "def update_prior(pmf, simultaneous_birthdays_observed):\n", " \"\"\"Updates the pmf with the posterior likelihood of `simultaneous_birthdays_observed`.\"\"\"\n", " l = likelihood(simultaneous_birthdays_observed, pmf.qs) # this is P(kB|N)\n", " l[pmf.qs < simultaneous_birthdays_observed] = 0\n", " pmf *= l\n", " pmf.normalize()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let's now proceed step by step and see how the successive evidence modifies our belief in the the most likely room size." ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "update_prior(pmf, 2) # we now know there's two people having a birthday on a particular day\n", "\n", "pmf.plot()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "As we expect from our introductory analysis, our first posterior is centered around a room size of 730, which is the most likely room size for two people sharing a birthday on a particular day." ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "update_prior(pmf, 1) # we now also know there's one person having a birthday on a particular day\n", "\n", "pmf.plot()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Taking into account one more information on a single birthday the probability gets shifted towards 365 (expected room size if you only know there's one person having a birthday on a particular day), while still retaining some shape of the previous estimate." ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "update_prior(pmf, 0) # we now also know there's zero people having a birthday on a particular day\n", "\n", "pmf.plot()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "And finally we shift further to the left (towards the expected value of 0 people when 0 zero people have a birthday on a particular day)." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This yields the solution to our problem. What is the most probable room size?" ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "365" ] }, "execution_count": 11, "metadata": {}, "output_type": "execute_result" } ], "source": [ "pmf.max_prob()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "And what is the 95% credible region?" ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([ 133., 1065.])" ] }, "execution_count": 12, "metadata": {}, "output_type": "execute_result" } ], "source": [ "pmf.credible_interval(0.95)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let's put all this together to draw a complete graph:" ] }, { "cell_type": "code", "execution_count": 13, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "first update [ 218. 1880.]\n", "second update [ 199. 1551.]\n", "third update [ 133. 1065.]\n" ] }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "hypos = np.arange(1, 2000)\n", "pmf = Pmf(1, hypos)\n", "pmf.normalize()\n", "\n", "fig, ax = plt.subplots(figsize=(10, 5))\n", "\n", "ax.plot(pmf.qs, pmf.ps, label='prior')\n", "\n", "update_prior(pmf, 2)\n", "print(\"first update\", pmf.credible_interval(.95))\n", "\n", "ax.plot(pmf.qs, pmf.ps, label='first update')\n", "\n", "update_prior(pmf, 1)\n", "print(\"second update\", pmf.credible_interval(.95))\n", "\n", "ax.plot(pmf.qs, pmf.ps, label='second update')\n", "\n", "update_prior(pmf, 0)\n", "print(\"third update\", pmf.credible_interval(.95))\n", "\n", "ax.plot(pmf.qs, pmf.ps, label='third update')\n", "\n", "\n", "\n", "ax.vlines(pmf.max_prob(), 0, pmf[pmf.max_prob()])\n", "\n", "mini, maxi = pmf.credible_interval(.95)\n", "sel = (pmf.qs > mini) & (pmf.qs <= maxi)\n", "ax.fill_between(pmf.qs[sel], pmf.ps[sel], alpha=0.5, label='95% credible region')\n", "ax.annotate(xy=(pmf.max_prob(), pmf.ps[pmf.max_prob()]), s=f\"{pmf.max_prob()}\",\n", " xytext=(0.3, 0.95), textcoords='axes fraction',\n", " arrowprops=dict(facecolor='black', shrink=0.05),\n", " horizontalalignment='right', verticalalignment='top')\n", "ax.set_xlabel('N')\n", "ax.set_ylabel('probability')\n", "ax.legend();" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "As you can see in the above plot having two birthdays observed shapes the posterior to center on 730 people, then observing one birthday moves it towards 365 and finally seeing zero born on another date shifts it towards 0. All things done, we end up with a most likely number of 365 people in the room." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Analytical solution " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "As my friend Anders has pointed out, there also exists an analytical solution to this problem. It works as follows: suppose the number of people in the room is N. What is the probability of observing 2, 1 and 0 conjoint birthdays? Since the events are independent, it is a multiplication of their likelihoods. As will notice, this is quite close to the expression derived using Bayes's theorem, but without the prior and without the normalizing constant in the denominator.\n", "\n", "$$\n", "L = P(2B | N) P(1B|N) P(0B|N)\n", "$$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let's compute this likelihood $L$ with `sympy`." ] }, { "cell_type": "code", "execution_count": 14, "metadata": {}, "outputs": [ { "data": { "text/latex": [ "$\\displaystyle \\frac{n^{2} p^{3} \\left(1 - p\\right)^{3 n - 3} \\left(n - 1\\right)}{2}$" ], "text/plain": [ "n**2*p**3*(1 - p)**(3*n - 3)*(n - 1)/2" ] }, "execution_count": 14, "metadata": {}, "output_type": "execute_result" } ], "source": [ "import sympy as sp\n", "\n", "n = sp.Symbol('n', integer=True, positive=True)\n", "p = sp.Symbol('p', positive=True)\n", "\n", "def likelihood_sympy(simultaneous_birthdays, n_people, p):\n", " return sp.binomial(n_people, simultaneous_birthdays) * p ** simultaneous_birthdays * (1 - p) ** (n_people - simultaneous_birthdays) \n", "\n", "l = likelihood_sympy(2, n, p) * likelihood_sympy(1, n, p) * likelihood_sympy(0, n, p) \n", "\n", "l = sp.simplify(l)\n", "\n", "l" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "(note: I have kept the probability of having a birthday on a particular day written as $p$ for now)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Once we have the likelihood, we want to maximize it. To do that, a necessary condition is that the derivative is zero. We can compute the derivative and solve the equation that sets it to 0 using the following code:" ] }, { "cell_type": "code", "execution_count": 15, "metadata": {}, "outputs": [ { "data": { "text/latex": [ "$\\displaystyle \\frac{- \\frac{\\sqrt{9 \\log{\\left(1 - p \\right)}^{2} + 6 \\log{\\left(1 - p \\right)} + 9}}{6} + \\frac{\\log{\\left(1 - p \\right)}}{2} - \\frac{1}{2}}{\\log{\\left(1 - p \\right)}}$" ], "text/plain": [ "(-sqrt(9*log(1 - p)**2 + 6*log(1 - p) + 9)/6 + log(1 - p)/2 - 1/2)/log(1 - p)" ] }, "execution_count": 15, "metadata": {}, "output_type": "execute_result" } ], "source": [ "sols = sp.solve(sp.Eq(l.diff(n), 0))\n", "\n", "sols[0][n]" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Finally, we can plug in the right value of $p$ and compute the analytical answer to the question of \"what is the most likely number of people in the room?\"." ] }, { "cell_type": "code", "execution_count": 16, "metadata": {}, "outputs": [ { "data": { "text/latex": [ "$\\displaystyle 364.8337149301$" ], "text/plain": [ "364.833714930100" ] }, "execution_count": 16, "metadata": {}, "output_type": "execute_result" } ], "source": [ "sols[0][n].subs({p:1/365})" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This is very close to our previous best estimate!" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can plot this expression to see how close the numerical results are (using an appropriate normalization). " ] }, { "cell_type": "code", "execution_count": 17, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "vals = sp.lambdify(n, l.subs({p:1/365}))(hypos) \n", "\n", "\n", "fig, ax = plt.subplots()\n", "ax.plot(hypos, vals / vals.max() * pmf.max(), label='analytical')\n", "ax.plot(pmf.qs[::10], pmf.ps[::10], 'x', label='bayesian solution')\n", "ax.legend();" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Indeed things seem to be very close. Let's see how close by computing the difference between the two curves." ] }, { "cell_type": "code", "execution_count": 18, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "delta = pmf.ps - vals / vals.max() * pmf.max()\n", "\n", "fig, ax = plt.subplots()\n", "ax.plot(pmf.qs, delta);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This is very small. \n", "\n", "So it seems that the two ways of solving the problem are very similar. However, there are differences. In particular, in the first method, we set the probability of seeing rooms larger than 2000 people to zero. It turns out that this doesn't seem to have an effect compared to the analytical solution.\n", "\n", "The analytical solution gives the impression that things are continuous in the number of people in the room (indeed, could it be that 364.83 people fit in a room?), whereas the first method restricts itself to a discrete setting (more appropriate in this case).\n", "\n", "Also, the analytical method didn't mention a prior. Is that a good or a bad thing? Well, it turns out that we implicitly used a prior in the analytical method, even though we didn't notice it. So I would argue it is a bad thing. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Conclusion" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "I hope you've like this little introduction to Bayesian statistics in times of the Coronavirus. If you're interested in this topic, I suggest you read Allen Downey's book, *Think Bayes* or follow him on Twitter." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

Tuesday is Bayes Day! And that means it's time for a new chapter from the in-progress second edition of Think Bayes: https://t.co/hHX6Ze3jgK

I think the exercises in this chapter are particularly good. I'll post solutions later this week.

— Allen Downey (@AllenDowney) June 16, 2020
" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**Acknowledgement** I would like to thank Allen Downey for his helpful comments on this post. All errors are, of course, mine." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "*This post was entirely written using the Jupyter Notebook. Its content is BSD-licensed. You can see a static view or download this notebook with the help of nbviewer at [20200624_BayesianInCoronaTimes.ipynb](http://nbviewer.ipython.org/urls/raw.github.com/flothesof/posts/master/20200624_BayesianInCoronaTimes.ipynb).*" ] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "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": "3.7.6" } }, "nbformat": 4, "nbformat_minor": 4 }