{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Learning goals\n", "\n", "Understand the following:\n", "\n", "- Probability distribution\n", "- Probability density function (PDF)\n", "- Gaussian distribution\n", "- Histogram\n", "- Mean\n", "- Standard deviation\n", "- Variance\n", "- Mode\n", "\n", "We will discuss these as we work through this example" ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", "import matplotlib.pyplot as plt\n", "import scipy.stats as stats" ] }, { "cell_type": "code", "execution_count": 17, "metadata": {}, "outputs": [], "source": [ "sample_size = 30\n", "\n", "true_mean = 10.0\n", "true_variance = 4.0\n", "true_std = np.sqrt(true_variance)\n", "\n", "rng = np.random.RandomState(123)\n", "fish_sample = rng.normal(loc=true_mean, scale=true_std, size=sample_size)" ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([ 7.82873879, 11.99469089, 10.565957 , 6.98741057, 8.8427995 ,\n", " 13.30287307, 5.14664151, 9.14217474, 12.53187252, 8.2665192 ,\n", " 8.6422277 , 9.81058206, 12.98277925, 8.72219601, 9.11203608,\n", " 9.13129745, 14.41186017, 14.37357218, 12.0081078 , 10.7723728 ,\n", " 11.47473715, 12.98146406, 8.12833226, 12.35165809, 7.49223866,\n", " 8.724497 , 11.81421039, 7.1426386 , 9.71986256, 8.27649021])" ] }, "execution_count": 8, "metadata": {}, "output_type": "execute_result" } ], "source": [ "fish_sample" ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "x=plt.hist(fish_sample)\n", "plt.xlabel(\"fish length (cm)\")\n", "plt.ylabel(\"counts\");" ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(array([1., 1., 3., 7., 4., 2., 2., 5., 3., 2.]),\n", " array([ 5.14664151, 6.07316338, 6.99968524, 7.92620711, 8.85272897,\n", " 9.77925084, 10.7057727 , 11.63229457, 12.55881644, 13.4853383 ,\n", " 14.41186017]),\n", " )" ] }, "execution_count": 10, "metadata": {}, "output_type": "execute_result" } ], "source": [ "x" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## What is the mean of the sample of fish lengths?" ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "10.089427941923741\n" ] } ], "source": [ "sample_mean = np.mean(fish_sample)\n", "print(sample_mean)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## What is the [mode](https://en.wikipedia.org/wiki/Mode_(statistics)) of the sample of fish lengths? (\"[modus](https://de.wikipedia.org/wiki/Modus_(Statistik))\" in German.)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## What is the sample variance of fish lengths?\n", "\n", "We put the result in the variable `length_variance`. We use the `ddof=1` keyword argument to `np.var()` because we are estimating variance from a sample here." ] }, { "cell_type": "code", "execution_count": 18, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "5.637780974408914\n" ] } ], "source": [ "sample_variance = np.var(fish_sample, ddof=1)\n", "print(sample_variance)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Probability Density Functions (PDFs)\n", "\n", "- for working with continuous variables (vs. probability mass functions for discrete variables)\n", "- here, the area under the curve gives the probability (in contrast to probability mass functions where we have probabilities for every single value)\n", "- the area under the whole curve is 1. In other words, some outcome must happen.\n", "\n", "## Normal Distribution (Gaussian Distribution)\n", "\n", "- unimodal and symmetric\n", "- many algorithms in machine learning & statistics have normality assumptions\n", "- two parameters: mean (center of the peak) and standard deviation (spread); $N(\\mu, \\sigma)$\n", "- we can estimate parameters $\\mu$ and $\\sigma$ by the sample mean ($\\bar{x})$ and sample variance ($s^2$)\n", "- univariate Normal distribution:\n", "\n", "$$N(\\mu, \\sigma) = f(x \\mid \\mu, \\sigma^2) = \\frac{1}{\\sqrt{2\\pi\\sigma^2}} \\; \\exp\\bigg(-\\frac{(x-\\mu)^2}{2\\sigma^2}\\bigg)$$\n", "\n", "- standard normal distribution with zero mean and unit variance, $N(0, 1)$:" ] }, { "cell_type": "code", "execution_count": 19, "metadata": {}, "outputs": [], "source": [ "def univariate_gaussian_pdf(x, mean, variance):\n", " return (1. / np.sqrt(2*np.pi*variance) * \n", " np.exp(- ((x - mean)**2 / (2.*variance))))" ] }, { "cell_type": "code", "execution_count": 20, "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "mean = 0\n", "stddev = 1\n", "x = np.arange(-5, 5, 0.01)\n", "y = univariate_gaussian_pdf(x, mean, stddev**2)\n", "plt.plot(x, y)\n", "plt.xlabel('x')\n", "plt.ylabel('Probability Density Function (PDF)')\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 21, "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "mean = 10\n", "stddev = 2.0\n", "x = np.arange(5, 15, 0.01)\n", "y = univariate_gaussian_pdf(x, mean, stddev**2)\n", "plt.plot(x, y)\n", "plt.xlabel('fish length (cm)')\n", "plt.ylabel('Probability Density Function (PDF)')\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 22, "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.hist(fish_sample, density=True, label='samples')\n", "\n", "x = np.linspace(5.0, 15.0, 100)\n", "y = univariate_gaussian_pdf(x, true_mean, true_variance)\n", "plt.plot(x, y, lw=5, label='theoretical (mean=%.1f, variance=%.1f)'%(true_mean,true_variance))\n", "\n", "sample_mean = np.mean(fish_sample)\n", "sample_variance = np.var(fish_sample, ddof=1) # for a sample variance, always use ddof=1. Here is one explanation why https://mortada.net/computing-sample-variance-why-divide-by-n-1.html\n", "y2 = univariate_gaussian_pdf(x, sample_mean, sample_variance)\n", "plt.plot(x, y2, label='empirical (mean=%.1f, variance=%.1f)'%(sample_mean,sample_variance))\n", "\n", "plt.xlabel(\"length (cm)\")\n", "plt.ylabel(\"probability\");\n", "plt.legend();\n", "# plt.savefig('fish-gaussian.png');" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Discussion points\n", "\n", "Here are a few questions you should be able to answer:\n", "\n", " - what is plotted on the x axis?\n", " - what is plotted on the y axis?\n", " - what is the area under the curve from -∞ to ∞?\n", " - according to our Guassian distribution, what is the most likely fish length?\n", " - according to our histogram, what is the most likely fish length?" ] } ], "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": "3.11.10" } }, "nbformat": 4, "nbformat_minor": 4 }