{ "cells": [ { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "Central Limit Theorem\n", "====\n", "\n", "## Unit 8, Lecture 1\n", "\n", "*Numerical Methods and Statistics*\n", "\n", "----\n", "\n", "#### Prof. Andrew White, March 20 2020" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "Central Limit Theorem (CLT)\n", "====\n", "\n", "Why are normal distributions common? They arise because when you sum multiple random variables, they become normally distributed if:\n", "\n", "1. They have finite means and variances\n", "2. You have enough of them (20-25 usually)\n" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "Each observation in our distribution, $x$, follows:\n", "\n", "$$x = \\frac{1}{N} \\sum_i^N r_i$$\n", "\n", "where $r_i$ are coming from the same distribution or different distributions. The CLT says if $N$ is big enough, $p(x)$ will be normally distributed regardless of how $p(r_i)$s are distributed." ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "slideshow": { "slide_type": "skip" } }, "outputs": [], "source": [ "%matplotlib inline\n", "import random\n", "from scipy import stats as ss\n", "import numpy as np\n", "import matplotlib.pyplot as plt\n", "import matplotlib as mpl\n", "import seaborn as sns\n", "from math import sqrt, pi\n", "def normal_pdf(x, mu, sigma):\n", " return 1 / (sigma * sqrt(2 * pi)) * np.exp(-(x - mu)**2 / (2. * sigma))\n", "mpl.style.use(['seaborn-notebook', 'seaborn-darkgrid'])\n" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "CLT Demonstration with Beta Distribution\n", "====\n", "\n", "Let's see the CLT with only 1 distribution. Note, CLT doesn't apply because $N=1$ is not sufficiently large. Take our only contributing distribution, $p(r_0)$ to be a beta distribution:\n", "$$\n", "p(r_0) = \\frac{1}{Z}\\, r_0^{\\alpha - 1} \\,(1 - r_0)^{\\beta - 1}\n", "$$\n", "\n", "Where $Z$, $\\alpha$, and $\\beta$ are parameters of the beta distribution. For the beta distribution, the sample space is $[0,1]$. Don't worry about this distribution; you don't need to know it! But it's *different* than the normal distribution." ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "Now consider our averaging equation:\n", "$$\n", "x = \\frac{1}{N} \\sum_i^N r_i\n", "$$\n", "\n", "\n", "We have $N = 1$ because we have one distribution, the beta distribution. What will $p(x)$ look like? Will it be normal?" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "fragment" } }, "source": [ "Not yet, becuase we have only $N = 1$. Let's try looking at $p(x)$. Instead of writing down the equation, we can instead use Python to *sample* realizations of $x$ many times and then histogram the results" ] }, { "cell_type": "code", "execution_count": 9, "metadata": { "slideshow": { "slide_type": "subslide" } }, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "data = np.empty(1000)\n", "#for 1000 times (enough to get a nice plot)\n", "for i in range(1000):\n", " data[i] = ss.beta.rvs(0.5, 0.5) \n", "\n", "\n", "#histogram the samples\n", "plt.hist(data, bins=25)\n", "plt.title('Average with N = 1')\n", "\n", "#Show the plot. \n", "plt.show() " ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "Remember that $N = 1$ means for each observation of $x$, we had 1 $r_i$ contributing to the average. Obviously this is silly, since $x$ = $r_1$, but let's see $N = 2$ where both $r_1$ and $r_2$ are the **same** beta distribution" ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "slideshow": { "slide_type": "subslide" } }, "outputs": [ { "data": { "image/png": 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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "#Sample 2 beta numbers 1000 times\n", "N = 2\n", "data = np.empty(1000)\n", "for i in range(1000):\n", " #Here's where we use the average equation\n", " r_1 = ss.beta.rvs(0.5, 0.5)\n", " r_2 = ss.beta.rvs(0.5, 0.5)\n", " data[i] = (r_1 + r_2) / 2\n", "\n", "#histogram the samples with 25 bins\n", "plt.hist(data, bins=25)\n", "plt.title('Average with N = 2')\n", "plt.show() " ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "Amazing! With $N = 2$ where already a little close. What's wrong with the domain though? How could this possibly be normal?!" ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "slideshow": { "slide_type": "subslide" } }, "outputs": [ { "data": { "image/png": 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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "#Sample 25 beta numbers 1000 times\n", "N = 25\n", "data = np.empty(1000)\n", "for i in range(1000):\n", " #Here's where we use the average equation\n", " #we'll do this more automatically using np.mean\n", " rs = ss.beta.rvs(0.5, 0.5, size=N)\n", " data[i] = np.mean(rs)\n", "\n", "#histogram the samples with 25 bins\n", "plt.hist(data, bins=25)\n", "plt.title('Average with N = 25')\n", "plt.show() " ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "As we increased the number of points contributing to the average, it eventually became a normal distribution!" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "CLT Demonstration with Multiple Binomial Distribution\n", "====\n", "\n", "We were able to move from a sample space from $[0,1]$ to make it appear to be $(-\\infty, \\infty)$. CLT also made a beta distribution, which has peaks at either end, become normal. Wow! Let's challenge it more. Consider sampling from a set of binomial distribututions and taking the average of the samples. Now we have multipled distributions and they're discrete!!" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "To remind ourselves, we're doing\n", "$$\n", "x = \\frac{1}{N} \\sum_i^N r_i\n", "$$\n", "\n", "where $r_i$ is sampled from $P_i(r_i)$, a set of **different** binomial distributions" ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "collapsed": true, "slideshow": { "slide_type": "subslide" } }, "outputs": [], "source": [ "N = 1\n", "\n", "#Create an array of p parameters to use for our distributions\n", "some_ps = np.random.random(N) \n", "\n", "#Create our M (trial number) parameters for binomial between 1 and 15.\n", "#We don't go past 15 because it's time consuming to compute the numbers\n", "some_Ms = np.random.randint(1, 15, N)\n", "\n", "#create a place to store our data\n", "data = []\n", "for i in range(10000):\n", " point = 0\n", " for j in range(N):\n", " #We use the jth distribution parameters to sample\n", " point += ss.binom.rvs(some_Ms[j], some_ps[j])\n", " #We cast to float, since everything is done until now in integers\n", " data.append(float(point) / N) " ] }, { "cell_type": "code", "execution_count": 7, "metadata": { "slideshow": { "slide_type": "subslide" } }, "outputs": [ { "data": { "image/png": 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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.hist(data, 25)\n", "plt.title('CLT with 1 Binomial Dist')\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "So it looks like a binomail distribution, as expected since $N = 1$. Meaning we have one binomial distribution" ] }, { "cell_type": "code", "execution_count": 8, "metadata": { "collapsed": true, "slideshow": { "slide_type": "subslide" } }, "outputs": [], "source": [ "N = 5\n", "\n", "#Create an array of p parameters to use for our distributions\n", "some_ps = np.random.random(N) \n", "\n", "#Create our M (trial number) parameters for binomial between 1 and 15.\n", "#We don't go past 15 because it's time consuming to compute the numbers\n", "some_Ms = np.random.randint(1, 15, N)\n", "\n", "#create a place to store our data\n", "data = []\n", "for i in range(10000):\n", " point = 0\n", " for j in range(N):\n", " #We use the jth distribution parameters to sample\n", " point += ss.binom.rvs(some_Ms[j], some_ps[j])\n", " #We cast to float, since everything is done until now in integers\n", " data.append(float(point) / N) " ] }, { "cell_type": "code", "execution_count": 9, "metadata": { "slideshow": { "slide_type": "subslide" } }, "outputs": [ { "data": { "image/png": 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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.hist(data, 25)\n", "plt.title('CLT with 5 Binomial Dist')\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 10, "metadata": { "collapsed": true, "slideshow": { "slide_type": "slide" } }, "outputs": [], "source": [ "N = 25\n", "\n", "#Create an array of p parameters to use for our distributions\n", "some_ps = np.random.random(N) \n", "\n", "#Create our M (trial number) parameters for binomial between 1 and 15.\n", "#We don't go past 15 because it's time consuming to compute the numbers\n", "some_Ms = np.random.randint(1, 15, N)\n", "\n", "#create a place to store our data\n", "data = []\n", "for i in range(10000):\n", " point = 0\n", " for j in range(N):\n", " #We use the jth distribution parameters to sample\n", " point += ss.binom.rvs(some_Ms[j], some_ps[j])\n", " #We cast to float, since everything is done until now in integers\n", " data.append(float(point) / N) " ] }, { "cell_type": "code", "execution_count": 11, "metadata": { "slideshow": { "slide_type": "subslide" } }, "outputs": [ { "data": { "image/png": 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hKyMZiWpeMqFw0xQj3vlnFY6eseCWaZn99u07WT/kcYtmZoc7NKKIwJozURAc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\nB9JT1PjGLfkw65OkDosopiWoFHh2+XT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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "sns.distplot(data)\n", "plt.title('CLT with 25 Binomial Dist')\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "Even though the component distributions are different and *discrete*, the average becomes a normal distribution!" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "CLT Trivia\n", "====\n", "\n", "Inidcate if the CLT applies to the following process:\n", "\n", "* You take the yearly rainfall in 25 counties in Rochester and compute their average.\n", "* You compute the average rainfall in a paricular city over the last 25 years.\n", "* You have 20 temperature sensors placed inside of a batch reactor and compute their average.\n", "* You measure the weight of 25 chemical samples\n", "* You eat 25 random candy bars per day and sum up their calories.\n", "* Your scale is inaccurate due to 20 sources of error (e.g, electrical circuit components air pressure, calibration). Assume their error is additive. You meausre the weight of something.\n", "* Your scale is not normally distributed. Each time you weigh something, you weigh it 22 times and take the average." ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "skip" } }, "source": [ "Yes, yes, yes, no (you did not average them), yes, yes, yes" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "Discovering the true mean\n", "====\n", "\n", "One important application of the CLT is describing the distribution of sample means. We want to specifically compare sample means with population means, $\\mu$. The word \"population\" means the statistics of an entire population of which we only see a small sample at any given time. You can also just think about it as the unknown probability distribution function that describes the samples we're observing. If we compuate a sample mean from a set of data from a population, it is described by:\n", "\n", "$$ p(\\bar{x})$$\n", "\n", "where $\\bar{x}$ is computed according to $$\\bar{x} = \\frac{1}{N} \\sum_i^N x_i$$\n", "\n", "Notice that it seems like $p(\\bar{x})$ normal due to CLT!" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "fragment" } }, "source": [ "This is a beautiful way of combining statistics and probability theory! We are doing sample means from some random data, $x_i$, which is a statistics problem and we're describing how this computation will look using probability theory." ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "Let's see what $p(\\bar{x})$ looks like. Is it normal? How does its standard deviation/variance change? Is it a function of sample size?" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "Rather than derive an equation for this, let's write a *program* which calculates sample means and see what happens.\n", "\n", "Let's see some code which calculates $\\bar{x}$ multiple times given that we know the true population $\\mu$. We will generate multiple samples of size $N$ and compute $\\bar{x}$. Then we'll histogram all the $\\bar{x}$s we see." ] }, { "cell_type": "code", "execution_count": 35, "metadata": { "collapsed": true, "slideshow": { "slide_type": "slide" } }, "outputs": [], "source": [ "def hist_means(N, mean=2, std_dev=3, bins=25, samples=10000):\n", " data = [] #we store results here\n", " #We're going through the process of computing a sample mean/var this many times\n", " for i in range(samples):\n", " #create N random samples.\n", " random_samples = ss.norm.rvs(loc=mean, scale=std_dev, size=N)\n", " #take their mean\n", " sample_mean = np.mean(random_samples)\n", " data.append(sample_mean)\n", " #After generating the data, we histogram with the given bin number\n", " hist, bins = np.histogram(data, bins, normed=True)\n", " #We compute the centers of the bins by averaging the intervals\n", " #that make up the bins\n", " bin_centers = (bins[1:] + bins[:-1]) / 2.\n", " return hist, bin_centers" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "Notice we picked $\\mu = 2$" ] }, { "cell_type": "code", "execution_count": 37, "metadata": { "slideshow": { "slide_type": "subslide" } }, "outputs": [ { "data": { "image/png": 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n5zwM7RMgdpybYu/vX1vnSO3b0ZcQiw2bq9VqaDQa0+3S0lL4+f3aw3jggQeg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\nMTQ6HitmXxB9Nwq63xeEZyiIyFR02mMsRh02PpS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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "hist, bin_centers = hist_means(N=25)\n", "plt.plot(bin_centers, hist)\n", "plt.title('Histogram of Sample Means with N = 25')\n", "plt.xlabel(r'$\\bar{x}$')\n", "plt.ylabel('Probability Density')\n", "plt.axvline(x=2)\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "As expected, we see that the distribution is normal with $N = 25$ samples. Also, we see that the distribution is centered on $\\mu$! So our guess for the distribution of $\\bar{x}$ is so far:\n", "\n", "**Guess 1**:\n", "$$\n", "p(\\bar{x}) = \\mathcal{N}(\\mu, ?)\n", "$$" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "To see what the standard deviation of sample mean is, let's try changing the *population* standard deviation" ] }, { "cell_type": "code", "execution_count": 46, "metadata": { "slideshow": { "slide_type": "subslide" } }, "outputs": [ { "data": { "image/png": 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4+Hi5Py2EGzUPc+WstvZunvn1exwprODqvFQ2fHs1EeEhjtfvv30hqUmxfLDz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\n3KDlg9A2/vGVgcGWAUzNH8kQSxF2teOMPDmC3oc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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "#These are the stddevs\n", "sigmas = [1, 2, 5, 10]\n", "#This creates a color function, using the summer palette\n", "color_map = plt.get_cmap(\"viridis\")\n", "#loop over sigmas\n", "for i in range(len(sigmas)):\n", " #call our function above\n", " hist, bin_centers = hist_means(25, mean=0, std_dev=sigmas[i])\n", " #plot the results, label it, and use our color function to get a color\n", " plt.plot(bin_centers, hist, color=color_map(i / len(sigmas)), label=\"$\\\\sigma={}$\".format(sigmas[i]))\n", "#add a plotting legend\n", "plt.legend()\n", "#set the x-axis limit\n", "plt.xlim(-3, 3)\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "It looks like a higher *population* standard deviation leads to more uncertainty in our estimate for $\\mu$. Our estaimte for $\\mu$ of course being $\\bar{x}$. Let's see if we can analytically describe this relationship. Let's guess that:\n", "\n", "**Guess 2:**\n", "$$\n", "p(\\bar{x}) \\propto \\mathcal{N}(\\mu, \\sigma)\n", "$$\n", "\n", "We're gussing that the CLT gives us a normal distribution centered at $0$ whose standard deviation is the population standard deviation. We can check this guess by converting the standard normal distribution:\n", "\n", "$$\n", "Z = \\frac{x - \\mu}{\\sigma}\n", "$$" ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "slideshow": { "slide_type": "subslide" } }, "outputs": [], "source": [ "def hist_means_scaled(N, mean=2, std_dev=3, bins=25, samples=10000):\n", " data = []\n", " for i in range(samples):\n", " random_samples = ss.norm.rvs(loc=mean, scale=std_dev, size=N)\n", " sample_mean = np.mean(random_samples)\n", " #The change!\n", " data.append((sample_mean - mean) / std_dev)\n", " hist, bins = np.histogram(data, bins, normed=True)\n", " bin_centers = (bins[1:] + bins[:-1]) / 2.\n", " return hist, bin_centers" ] }, { "cell_type": "code", "execution_count": 42, "metadata": { "slideshow": { "slide_type": "subslide" } }, "outputs": [ { "data": { "image/png": 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eH4hAlhSoWdnoUs5on3mSgUxUdBNesj506BAef/xxdHd3QxRF7N69G9dccw2a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\nMAVNtOGtP7xtcEVE5sVAJiq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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "sigmas = [1, 2, 5, 10]\n", "color_map = plt.get_cmap(\"viridis\")\n", "for i in range(len(sigmas)):\n", " hist, bin_centers = hist_means_scaled(25, std_dev=sigmas[i])\n", " plt.plot(bin_centers, hist, color=color_map(i / len(sigmas)), label=\"$\\\\sigma={}$\".format(sigmas[i]))\n", "plt.legend()\n", "plt.xlim(-3, 3)\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "Jackpot! Now we now how to describe $p(\\bar{x})$. However, we haven't assessed the effect of the number of samples! How does $N$ affect it?" ] }, { "cell_type": "code", "execution_count": 10, "metadata": { "slideshow": { "slide_type": "subslide" } }, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "#These are the sample sizes we'll try out\n", "Ns = [5, 10, 15, 20, 100]\n", "color_map = plt.get_cmap(\"viridis\")\n", "for i in range(len(Ns)):\n", " hist, bin_centers = hist_means_scaled(Ns[i])\n", " plt.plot(bin_centers, hist, color=color_map(i / len(Ns)), label=\"$N={}$\".format(Ns[i]))\n", "plt.legend()\n", "plt.xlim(-3, 3)\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "This looks like what happened, that there is a scaling effect. It turns out, the effect is similar:\n", "\n", "$$\n", "p(\\bar{x}) = \\mathcal{N}\\left(\\mu, \\frac{\\sigma}{\\sqrt{N}}\\right)\n", "$$\n", "\n", "This is indeed the answer. " ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "We will often discuss the uncertainty in the population mean. That means how well we know the opulation mean. This is $p(\\bar{x} - \\mu)$. Using the knowledge above, we can see that:\n", "\n", "$$\n", "p(\\bar{x} - \\mu) = \\mathcal{N}\\left(0, \\frac{\\sigma}{\\sqrt{N}}\\right)\n", "$$\n", "\n", "One interesting attribute is that we can view either $\\bar{x}$ as the variable or $\\mu$ as the variable. If we view $\\mu$ as the variable, we're describing where we think the population mean might be. If, on the other hand, we view $\\bar{x}$ as the variable, we're describing where our sample mean will be if we take a sample." ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "We will use the words uncertatiny and error as synonyms. " ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "fragment" } }, "source": [ "The error in population mean is a normal distribution with ${\\cal N} (0, \\sigma / \\sqrt{N})$ where $\\sigma$ is the true/population $\\sigma$. We usually call the standard deviation of this distribution the \"standard error\":\n", "\n", "$$\\sigma_e = \\frac{\\sigma}{\\sqrt{N}} $$\n", "\n", "*later we'll see that we must estimate $\\sigma$ if we do not know it by computing the sample standard deviation. Then the standard error becomes $\\sigma_x / \\sqrt{N}$. We still call it standard error because standard error means the standard deviation in the error distribution, $p(\\bar{x} - \\mu)$.*" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "Analytical Equation for Error in Population Mean\n", "----\n", "\n", "We saw above how things look when we histogram and sample. That gave us an empirical look at how the sample mean varies relative to the population mean. Let's now see our analytical equation above compare with the histograms." ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "As stated above, using our sample mean to estimate our population mean leads to a probability distribution:\n", "\n", "$$\n", "p(\\bar{x} - \\mu) = \\mathcal{N}(0, \\sigma / \\sqrt{N}) = \\frac{\\sqrt{N}}{\\sqrt{\\sigma^2 2\\pi}} e^{-\\frac{\\bar{x}^2}{\\sigma^2 / N}}\n", "$$\n", "\n", "**where now we'll take the variable we do not know (the random variable) as as the population mean ($\\mu$)**" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "Let's compare our empirical estimates above to this:" ] }, { "cell_type": "code", "execution_count": 11, "metadata": { "slideshow": { "slide_type": "subslide" } }, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "pop_std = 1\n", "\n", "#this is the code from above\n", "for i in range(len(Ns)):\n", " Ni = Ns[i]\n", " hist, bin_centers = hist_means_scaled(Ni, std_dev=pop_std, samples=25000) \n", " plt.plot(bin_centers, hist, color=color_map(i / len(Ns)), label=\"$N={}$\".format(Ni))\n", " #plot analytic\n", " #make some points that span the high-probability density values\n", " standard_error = pop_std / np.sqrt(Ni)\n", " x = np.linspace(- 5*standard_error, 5 * standard_error, 500)\n", " plt.plot(x, ss.norm.pdf(x, scale=standard_error), color=color_map(i / len(Ns)), label=\"Analytic $N={}$\".format(Ni), linestyle='--')\n", "plt.legend()\n", "plt.xlim(-1, 1)\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "So it is true that $p(\\bar{x} - \\mu)$ follows a normal distribution when we know the population standard deviation!" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "Error in Population Mean - Example Problem\n", "====\n", "\n", "I know that $\\sigma = 0.2$ g for a chemical balance. I am calibrating my micro-pipettes which requires me to weigh out a volume of water. I weigh out 1 ml of water 20 times with a micro-pipette. The sample mean is 1.001 g. What is the probability the true mean of the micro-pipette is within 0.001 g of the sample mean?" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "fragment" } }, "source": [ "This is a normal distribution with ${\\cal N} (0, \\sqrt{0.2^2 / 20})$ and I want the interval between -0.001 and 0.001." ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "$\\DeclareMathOperator{\\erf}{erf}$\n", "$\\DeclareMathOperator{\\cdf}{CDF}$\n", "$$\\int_{Z_1}^{Z_2} {\\cal N}(0, 1) = \\cdf(Z_2) - \\cdf(Z_1)$$" ] }, { "cell_type": "code", "execution_count": 12, "metadata": { "slideshow": { "slide_type": "fragment" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "0.0178397545029\n" ] } ], "source": [ "from math import sqrt\n", "\n", "sigma = sqrt(0.2**2 / 20)\n", "Z1 = -0.001 / sigma\n", "Z2 = -Z1\n", "\n", "print( ss.norm.cdf(Z2) - ss.norm.cdf(Z1))" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "Unkown Population Standard Deviation\n", "====\n", "What if we do not have the population variance or standard deviation and we're estimating it at the same time? Let's explore to see if it's still normal.\n", "\n", "**Now we include the $1/N$ term we observed previously, so that we remove the influence of sampling.**" ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "slideshow": { "slide_type": "subslide" } }, "outputs": [], "source": [ "def make_hist(N, mean=12, std_dev=3, bins=25, samples=100000):\n", " data = []\n", " for i in range(samples):\n", " random_samples = np.random.normal(mean, std_dev, N) \n", " sample_mean = np.mean(random_samples)\n", " sample_var = np.var(random_samples) * (N / (N - 1.0))\n", " #We add the sqrt(N) dependence below\n", " data.append((sample_mean - mean) / (sqrt(sample_var) / sqrt(N)))\n", " hist, bins = np.histogram(data, bins = np.linspace(-3, 3, bins))\n", " bin_centers = (bins[1:] + bins[:-1]) / 2.\n", " #This line we changed so that we're working in probability, not counts.\n", " return hist / samples, bin_centers" ] }, { "cell_type": "code", "execution_count": 15, "metadata": { "slideshow": { "slide_type": "subslide" } }, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "Ns = [3, 5, 10, 25, 100]\n", "color_map = plt.get_cmap('summer')\n", "for i in range(len(Ns)):\n", " Ni = Ns[i]\n", " hist, bin_centers = make_hist(Ni, std_dev=1)\n", " plt.plot(bin_centers, hist, color=color_map(i / len(Ns)), label='$N={}$'.format(Ni))\n", "\n", "from math import erf\n", "x = np.linspace(-3,3,25)\n", "#The extra factor is to scale the pdf to match our data\n", "plt.plot(x,normal_pdf(x, 0, 1) / (erf(3 / sqrt(2)) - \\\n", " erf(-3 / sqrt(2))) / 2,\n", " label=\"Normal\", color='red')\n", " \n", "plt.legend()\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "Does Unknown Population Standard Deviation and Mean Obey CLT?\n", "====\n", "\n", "**Not until ~25 samples**. If the sample size is smaller, assuming a normal distribution gives too conservative of intervals. Note that CLT applies whenever we know population standard deviation. It does not with small sample number and when we're estimating both the sample mean and sample standard deviation." ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "Student's t-distribution\n", "====\n", "The distribution which describes the distance between the sample and true mean (population mean) when we do not know standard deviation is called the Student's $t$-distribution." ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "$p(\\mu - \\bar{x})$ follows a $t$-distribution with $\\sigma_e = \\sigma_x / \\sqrt{N}$. \n", "\n", "\n", "$$p(\\mu - \\bar{x}) = T(0, \\sigma_x / \\sqrt{N}, N - 1)$$\n", "\n", "Note that this takes in additional parameter, $N - 1$. This is the degrees of freedom, which just like in variance we need to subtract one from. " ] }, { "cell_type": "code", "execution_count": 17, "metadata": { "slideshow": { "slide_type": "subslide" } }, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import scipy.stats\n", "\n", "#make some points\n", "x = np.linspace(-5,5, 100)\n", "\n", "#Compute pdf on t and normal\n", "yn = scipy.stats.norm.pdf(x)\n", "for i,Ni in enumerate(Ns):\n", " y = scipy.stats.t.pdf(x, df=Ni-1)\n", " plt.plot(x,y,color=color_map(i / len(Ns)),label=\"T, N = {}\".format(Ni)) \n", "plt.plot(x,yn, color='r',label=\"Normal\")\n", "plt.legend()\n", "\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "Summary\n", "====\n", "\n", "Estimating the population mean from a sample mean is a random distribution. The sample mean, $\\bar{x}$, is a statistic and $\\mu$ is a random variable which follows either a normal or $t$-distribution. " ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "When we know the population standard deviation, $p(\\mu) = {\\mathcal N}(\\bar{x}, \\sigma / \\sqrt{N})$ where $N$ is the number of samples we used to calculate the sample mean and $\\sigma$ is the population standard deviation. " ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "When we do not know the population standard deviation, there is some additional error/uncertainty because we are estimating the population standard deviation with a sample standard deviation. Using $\\sigma_x$ to indicate the sample standard deviation: $p(\\mu) = T(\\bar{x}, \\sigma_x / \\sqrt{N}, N-1)$. Notice the $t$-distribution depends on the number of samples. The third term, N-1, is the degrees of freedom." ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "The standard deviations of these distributions is $\\sigma / \\sqrt{N}$ or $\\sigma_x / \\sqrt{N}$. To reduce confusion of the fact that the standard deviation of the distribution for the population mean is different than the population standard devition, sometimes this is called the standard error:\n", "\n", "$$\n", "\\sigma_e = \\frac{\\sigma}{\\sqrt{N}}\\; \\textrm{or} \\; \\frac{\\sigma_x}{\\sqrt{N}}\n", "$$" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "Now we know the probability distribution for the population mean, so that we can do things like calculate probabilities of intervals or plot probability densities of where the true mean lies." ] } ], "metadata": { "celltoolbar": "Slideshow", "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": "3.7.3" } }, "nbformat": 4, "nbformat_minor": 1 }