From 787b1fc99f0afe728496e9313abc5cc4d99beae1 Mon Sep 17 00:00:00 2001 From: Allen Downey Date: Sun, 17 Dec 2023 22:36:22 -0500 Subject: [PATCH] Adding bookstore --- examples/bookstore.ipynb | 301 ++++++++++++++++++++++++++------------- 1 file changed, 200 insertions(+), 101 deletions(-) diff --git a/examples/bookstore.ipynb b/examples/bookstore.ipynb index c0d016d8..69c75e70 100644 --- a/examples/bookstore.ipynb +++ b/examples/bookstore.ipynb @@ -4,18 +4,28 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "# Think Bayes\n", + "# How Many Books?\n", "\n", - "Second Edition\n", + "Suppose you are the author of a book like *Probably Overthinking It*, and when you visit a local bookstore, like Newtonville Books in Newton, MA, you see that they have two copies of your book on display.\n", "\n", - "Copyright 2020 Allen B. Downey\n", + "Is it good that they have only a few copies, because it suggests they started with more and sold some? Or is it bad because it suggests they only keep a small number in stock, and they have not sold. More generally, what number of books would you like to see?\n", "\n", - "License: [Attribution-NonCommercial-ShareAlike 4.0 International (CC BY-NC-SA 4.0)](https://creativecommons.org/licenses/by-nc-sa/4.0/)" + "To answer these questions, we have to make some modeling decisions. To keep it simple, I'll assume:\n", + "\n", + "* The bookstore orders books on some regular cycle of unknown duration.\n", + "\n", + "* At the beginning of every cycle, they start with `k` books.\n", + "\n", + "* People buy the book at a rate of `λ` books per cycle.\n", + "\n", + "* When you visit the store, you arrive at a random time `t` during the cycle.\n", + "\n", + "We'll start by defining prior distributions for these parameters, and then we'll update it with the observed data. Here are some libraries we'll need." ] }, { "cell_type": "code", - "execution_count": 1, + "execution_count": 73, "metadata": {}, "outputs": [], "source": [ @@ -31,24 +41,21 @@ }, { "cell_type": "code", - "execution_count": 2, + "execution_count": 74, "metadata": {}, "outputs": [], "source": [ - "# Get utils.py and create directories\n", + "# Get utils.py\n", "\n", "import os\n", "\n", "if not os.path.exists('utils.py'):\n", - " !wget https://github.com/AllenDowney/ThinkBayes2/raw/master/soln/utils.py\n", - " \n", - "if not os.path.exists('figs'):\n", - " !mkdir figs" + " !wget https://github.com/AllenDowney/ThinkBayes2/raw/master/soln/utils.py" ] }, { "cell_type": "code", - "execution_count": 3, + "execution_count": 75, "metadata": {}, "outputs": [], "source": [ @@ -57,12 +64,21 @@ "import matplotlib.pyplot as plt\n", "\n", "from empiricaldist import Pmf\n", - "from utils import decorate, savefig" + "from utils import decorate" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Priors\n", + "\n", + "For some books, the store only keeps one copy in stock. For others it might keep as many as ten. If we would be equally unsurprised by any value in this range, the prior distribution of `k` is uniform between `1` and `10`." ] }, { "cell_type": "code", - "execution_count": 4, + "execution_count": 76, "metadata": {}, "outputs": [], "source": [ @@ -72,9 +88,16 @@ "prior_k.index.name = 'k'" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "If we arrive at a random point in the cycle, the prior distribution of `t` is uniform between `0` and `1`, measured in cycles." + ] + }, { "cell_type": "code", - "execution_count": 5, + "execution_count": 77, "metadata": {}, "outputs": [], "source": [ @@ -84,9 +107,17 @@ "prior_t.index.name = 't'" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Now let's figure the book-buying rate is probably between `2` and `3` copies per cycle, but it could be substantially higher -- with low probability.\n", + "We can choose a lognormal distribution that has a mean and shape that seem reasonable." + ] + }, { "cell_type": "code", - "execution_count": 6, + "execution_count": 78, "metadata": {}, "outputs": [ { @@ -95,7 +126,7 @@ "2.7952013319456332" ] }, - "execution_count": 6, + "execution_count": 78, "metadata": {}, "output_type": "execute_result" } @@ -116,9 +147,16 @@ "prior_lambda.mean()" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Here's what it looks like." + ] + }, { "cell_type": "code", - "execution_count": 7, + "execution_count": 79, "metadata": {}, "outputs": [ { @@ -137,31 +175,65 @@ "decorate()" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "To form the joint prior distribution, I'll use `meshgrid` with the `ij` indexing order, which makes the order of the dimensions the same as the order of the arguments: `k`, `λ`, `t`." + ] + }, { "cell_type": "code", - "execution_count": 8, + "execution_count": 116, + "metadata": {}, + "outputs": [], + "source": [ + "def meshgrid(*args, **options):\n", + " if 'indexing' not in options:\n", + " options['indexing'] = 'ij'\n", + " return np.meshgrid(*args, **options)" + ] + }, + { + "cell_type": "code", + "execution_count": 117, "metadata": {}, "outputs": [ { "data": { "text/plain": [ - "(50, 10, 21)" + "(10, 50, 21)" ] }, - "execution_count": 8, + "execution_count": 117, "metadata": {}, "output_type": "execute_result" } ], "source": [ - "PK, PLAMBDA, PT = np.meshgrid(prior_k, prior_lambda, prior_t)\n", + "PK, PLAMBDA, PT = meshgrid(prior_k, prior_lambda, prior_t)\n", "prior = PK * PLAMBDA * PT\n", "prior.shape" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## The update\n", + "\n", + "Now for the update, we have to handle two cases:\n", + "\n", + "* If we observe at least one book, `n`, the probability of the data is the probability of selling `k-n` book at rate `λ` over period `t`, which is given by the Poisson PMF.\n", + "\n", + "* If we see that there are no copies left, we have to add in the probability that the number of books sold in this period could have exceeded `k`, which is given by the Poisson survival function.\n", + "\n", + "The following function computes the probability of the data for all values of the parameters, multiplies by the prior, and normalizes the result." + ] + }, { "cell_type": "code", - "execution_count": 9, + "execution_count": 82, "metadata": {}, "outputs": [], "source": [ @@ -170,13 +242,11 @@ "def update(prior, data):\n", " n = data\n", " \n", - " # TODO: special case n==0\n", - "\n", - " K, LAMBDA, T = np.meshgrid(ks, lambdas, ts)\n", + " K, LAMBDA, T = meshgrid(ks, lambdas, ts)\n", " \n", " like = poisson(mu=LAMBDA*T).pmf(K-n)\n", " if n == 0:\n", - " like += poisson(mu=LAMBDA*T).sf(K-n)\n", + " like += poisson(mu=LAMBDA*T).sf(K)\n", "\n", " posterior = prior * like\n", " posterior /= posterior.sum()\n", @@ -184,47 +254,68 @@ " return posterior" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "As an example, we'll do an update with the hypothetically observed `2` books." + ] + }, { "cell_type": "code", - "execution_count": 13, + "execution_count": 119, "metadata": {}, "outputs": [], "source": [ - "n = 3\n", + "n = 2\n", "posterior = update(prior, n)" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "From the joint posterior, we can extract the marginal distributions of `k` and `λ`, and compute their means." + ] + }, { "cell_type": "code", - "execution_count": 14, + "execution_count": 120, "metadata": {}, "outputs": [ { "data": { "text/plain": [ - "(4.25472830442544, 2.693603624832523)" + "(3.294088962095148, 2.720709517121936)" ] }, - "execution_count": 14, + "execution_count": 120, "metadata": {}, "output_type": "execute_result" } ], "source": [ - "marginal_k = Pmf(posterior.sum(axis=(0, 2)), ks)\n", - "marginal_lambda = Pmf(posterior.sum(axis=(1, 2)), lambdas)\n", + "posterior_k = Pmf(posterior.sum(axis=(1, 2)), ks)\n", + "posterior_lambda = Pmf(posterior.sum(axis=(0, 2)), lambdas)\n", "\n", - "marginal_k.mean(), marginal_lambda.mean()" + "posterior_k.mean(), posterior_lambda.mean()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Seeing two books suggests that the store starts each cycle with 3-4 books and sells 2-3 per cycle. Here's the posterior distribution of `k` compared to its prior." ] }, { "cell_type": "code", - "execution_count": 15, + "execution_count": 123, "metadata": {}, "outputs": [ { "data": { - "image/png": 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", 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", "text/plain": [ "
" ] @@ -235,18 +326,27 @@ ], "source": [ "prior_k.plot(label=f'prior', color='gray')\n", - "marginal_k.plot(label=f'n = {n}')\n", - "decorate(title='Posterior distribution of k')" + "posterior_k.plot(label=f'n = {n}')\n", + "decorate(xlabel='Number of books, k',\n", + " ylabel='PMF',\n", + " title='Posterior distribution of k')" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "And here's the posterior distribution of `λ`." ] }, { "cell_type": "code", - "execution_count": 16, + "execution_count": 122, "metadata": {}, "outputs": [ { "data": { - "image/png": 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", + "image/png": 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", "text/plain": [ "
" ] @@ -257,13 +357,34 @@ ], "source": [ "prior_lambda.plot(label='prior', color='gray')\n", - "marginal_lambda.plot(label=f'n = {n}')\n", - "decorate(title='Posterior distribution of lambda')" + "posterior_lambda.plot(label=f'n = {n}')\n", + "decorate(xlabel='Book-selling rate, λ',\n", + " ylabel='PMF',\n", + " title='Posterior distribution of lambda')" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Seeing two books doesn't provide much information about the book-selling rate." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Optimization\n", + "\n", + "Now let's consider the more general question, \"What number of books would you most like to see?\" There are two ways we might answer:\n", + "\n", + "* The observation that leads to the highest estimate of `λ` might seem to be the best. However, that ignore an interaction between `k` and ``\n", + " `" ] }, { "cell_type": "code", - "execution_count": 51, + "execution_count": 87, "metadata": {}, "outputs": [], "source": [ @@ -277,7 +398,7 @@ }, { "cell_type": "code", - "execution_count": 52, + "execution_count": 88, "metadata": {}, "outputs": [ { @@ -298,33 +419,33 @@ }, { "cell_type": "code", - "execution_count": 53, + "execution_count": 91, "metadata": {}, "outputs": [], "source": [ "def compute_sales(posterior):\n", - " marginal_joint = posterior.sum(axis=2)\n", - " marginal_joint.shape\n", + " posterior_joint = posterior.sum(axis=2)\n", + " posterior_joint.shape\n", "\n", - " K, LAMBDA = np.meshgrid(ks, lambdas)\n", + " K, LAMBDA = meshgrid(ks, lambdas)\n", " K.shape\n", "\n", - " SALES = marginal_joint * np.minimum(K, LAMBDA)\n", + " SALES = posterior_joint * np.minimum(K, LAMBDA)\n", " return np.sum(SALES)" ] }, { "cell_type": "code", - "execution_count": 54, + "execution_count": 92, "metadata": {}, "outputs": [ { "data": { "text/plain": [ - "2.048177523297997" + "2.449169695342132" ] }, - "execution_count": 54, + "execution_count": 92, "metadata": {}, "output_type": "execute_result" } @@ -335,15 +456,16 @@ }, { "cell_type": "code", - "execution_count": 59, + "execution_count": 100, "metadata": {}, "outputs": [], "source": [ "def compute_sales(posterior):\n", - " marginal_joint = pd.DataFrame(posterior.sum(axis=2), index=lambdas, columns=ks)\n", + " posterior_joint = pd.DataFrame(posterior.sum(axis=2), \n", + " index=ks, columns=lambdas)\n", "\n", " res = []\n", - " for (lam, k), p in marginal_joint.stack().items():\n", + " for (k, lam), p in posterior_joint.stack().items():\n", " exp_sales = make_poisson(lam, k).mean()\n", " res.append((exp_sales, p))\n", " \n", @@ -354,16 +476,16 @@ }, { "cell_type": "code", - "execution_count": 60, + "execution_count": 101, "metadata": {}, "outputs": [ { "data": { "text/plain": [ - "2.0372943847605636" + "2.2695775366862856" ] }, - "execution_count": 60, + "execution_count": 101, "metadata": {}, "output_type": "execute_result" } @@ -374,7 +496,7 @@ }, { "cell_type": "code", - "execution_count": 61, + "execution_count": 103, "metadata": {}, "outputs": [], "source": [ @@ -382,17 +504,17 @@ "\n", "for n in range(11):\n", " posterior = update(prior, n)\n", - " marginal_k = Pmf(posterior.sum(axis=(0, 2)), ks)\n", - " marginal_lambda = Pmf(posterior.sum(axis=(1, 2)), lambdas)\n", + " posterior_k = Pmf(posterior.sum(axis=(1, 2)), ks)\n", + " posterior_lambda = Pmf(posterior.sum(axis=(0, 2)), lambdas)\n", "\n", - " k, lam = marginal_k.mean(), marginal_lambda.mean()\n", + " k, lam = posterior_k.mean(), posterior_lambda.mean()\n", " sales = compute_sales(posterior)\n", " res.append((n, k, lam, sales))" ] }, { "cell_type": "code", - "execution_count": 65, + "execution_count": 104, "metadata": {}, "outputs": [ { @@ -519,7 +641,7 @@ "10 10 10.000000 2.056530 2.037294" ] }, - "execution_count": 65, + "execution_count": 104, "metadata": {}, "output_type": "execute_result" } @@ -531,7 +653,7 @@ }, { "cell_type": "code", - "execution_count": 67, + "execution_count": 105, "metadata": {}, "outputs": [ { @@ -553,7 +675,7 @@ }, { "cell_type": "code", - "execution_count": 70, + "execution_count": 106, "metadata": {}, "outputs": [ { @@ -562,7 +684,7 @@ "5" ] }, - "execution_count": 70, + "execution_count": 106, "metadata": {}, "output_type": "execute_result" }, @@ -586,44 +708,21 @@ }, { "cell_type": "code", - "execution_count": 63, + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + }, + { + "cell_type": "markdown", "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "\n", - "array([[0.67563753, 0.20865251, 0.11984538, 0.11573044],\n", - " [0.06685941, 0.34505141, 0.83588825, 0.90362598],\n", - " [0.12914904, 0.9271302 , 0.80307685, 0.67546577]])\n", - "Coordinates:\n", - " * latitude (latitude) int64 10 20 30\n", - " * longitude (longitude) int64 100 110 120 130\n" - ] - } - ], "source": [ - "import xarray as xr\n", - "import numpy as np\n", - "\n", - "# Create a 2D DataArray using a dictionary for dimensions and coordinates\n", - "data = np.random.rand(3, 4)\n", - "coordinates = {'latitude': [10, 20, 30], 'longitude': [100, 110, 120, 130]}\n", + "Thanks to Aubrey Clayton for [this tweet], which gave me the idea for this article.\n", "\n", - "# Create the 2D DataArray\n", - "data_array_2d = xr.DataArray(data, coords=coordinates.items(), dims=coordinates.keys())\n", + "Copyright 2023 Allen B. Downey\n", "\n", - "# Display the 2D DataArray\n", - "print(data_array_2d)\n" + "License: [Attribution-NonCommercial-ShareAlike 4.0 International (CC BY-NC-SA 4.0)](https://creativecommons.org/licenses/by-nc-sa/4.0/)" ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": {}, - "outputs": [], - "source": [] } ], "metadata": {