diff --git a/notebooks/Normal and t-Distribution/BIND_2_1_and_2_2.ipynb b/notebooks/Normal and t-Distribution/BIND_2_1_and_2_2.ipynb new file mode 100644 index 0000000000000000000000000000000000000000..b02e5211f0c9b8708ac2c4d37404bae000b2a3f5 --- /dev/null +++ b/notebooks/Normal and t-Distribution/BIND_2_1_and_2_2.ipynb @@ -0,0 +1,669 @@ +{ + "cells": [ + { + "cell_type": "code", + "execution_count": 2, + "metadata": { + "tags": [] + }, + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "WARNING (pytensor.tensor.blas): Using NumPy C-API based implementation for BLAS functions.\n" + ] + } + ], + "source": [ + "import scipy.stats as st\n", + "import matplotlib.pyplot as plt\n", + "import numpy as np\n", + "import pandas as pd\n", + "import warnings \n", + "warnings.filterwarnings(\"ignore\")\n", + "import arviz as az\n", + "import pymc as pm\n", + "import scipy.stats as st" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Wir lesen den Datensatz `students.csv` ein und betrachten die ersten Zeilen des Dataframes." + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": { + "tags": [] + }, + "outputs": [ + { + "data": { + "text/html": [ + "<div>\n", + "<style scoped>\n", + " .dataframe tbody tr th:only-of-type {\n", + " vertical-align: middle;\n", + " }\n", + "\n", + " .dataframe tbody tr th {\n", + " vertical-align: top;\n", + " }\n", + "\n", + " .dataframe thead th {\n", + " text-align: right;\n", + " }\n", + "</style>\n", + "<table border=\"1\" class=\"dataframe\">\n", + " <thead>\n", + " <tr style=\"text-align: right;\">\n", + " <th></th>\n", + " <th>stud.id</th>\n", + " <th>name</th>\n", + " <th>gender</th>\n", + " <th>age</th>\n", + " <th>height</th>\n", + " <th>weight</th>\n", + " <th>religion</th>\n", + " <th>nc.score</th>\n", + " <th>semester</th>\n", + " <th>major</th>\n", + " <th>minor</th>\n", + " <th>score1</th>\n", + " <th>score2</th>\n", + " <th>online.tutorial</th>\n", + " <th>graduated</th>\n", + " <th>salary</th>\n", + " </tr>\n", + " </thead>\n", + " <tbody>\n", + " <tr>\n", + " <th>1</th>\n", + " <td>833917</td>\n", + " <td>Gonzales, Christina</td>\n", + " <td>Female</td>\n", + " <td>19</td>\n", + " <td>160</td>\n", + " <td>64.8</td>\n", + " <td>Muslim</td>\n", + " <td>1.91</td>\n", + " <td>1st</td>\n", + " <td>Political Science</td>\n", + " <td>Social Sciences</td>\n", + " <td>NaN</td>\n", + " <td>NaN</td>\n", + " <td>0</td>\n", + " <td>0</td>\n", + " <td>NaN</td>\n", + " </tr>\n", + " <tr>\n", + " <th>2</th>\n", + " <td>898539</td>\n", + " <td>Lozano, T'Hani</td>\n", + " <td>Female</td>\n", + " <td>19</td>\n", + " <td>172</td>\n", + " <td>73.0</td>\n", + " <td>Other</td>\n", + " <td>1.56</td>\n", + " <td>2nd</td>\n", + " <td>Social Sciences</td>\n", + " <td>Mathematics and Statistics</td>\n", + " <td>NaN</td>\n", + " <td>NaN</td>\n", + " <td>0</td>\n", + " <td>0</td>\n", + " <td>NaN</td>\n", + " </tr>\n", + " <tr>\n", + " <th>3</th>\n", + " <td>379678</td>\n", + " <td>Williams, Hanh</td>\n", + " <td>Female</td>\n", + " <td>22</td>\n", + " <td>168</td>\n", + " <td>70.6</td>\n", + " <td>Protestant</td>\n", + " <td>1.24</td>\n", + " <td>3rd</td>\n", + " <td>Social Sciences</td>\n", + " <td>Mathematics and Statistics</td>\n", + " <td>45.0</td>\n", + " <td>46.0</td>\n", + " <td>0</td>\n", + " <td>0</td>\n", + " <td>NaN</td>\n", + " </tr>\n", + " <tr>\n", + " <th>4</th>\n", + " <td>807564</td>\n", + " <td>Nem, Denzel</td>\n", + " <td>Male</td>\n", + " <td>19</td>\n", + " <td>183</td>\n", + " <td>79.7</td>\n", + " <td>Other</td>\n", + " <td>1.37</td>\n", + " <td>2nd</td>\n", + " <td>Environmental Sciences</td>\n", + " <td>Mathematics and Statistics</td>\n", + " <td>NaN</td>\n", + " <td>NaN</td>\n", + " <td>0</td>\n", + " <td>0</td>\n", + " <td>NaN</td>\n", + " </tr>\n", + " <tr>\n", + " <th>5</th>\n", + " <td>383291</td>\n", + " <td>Powell, Heather</td>\n", + " <td>Female</td>\n", + " <td>21</td>\n", + " <td>175</td>\n", + " <td>71.4</td>\n", + " <td>Catholic</td>\n", + " <td>1.46</td>\n", + " <td>1st</td>\n", + " <td>Environmental Sciences</td>\n", + " <td>Mathematics and Statistics</td>\n", + " <td>NaN</td>\n", + " <td>NaN</td>\n", + " <td>0</td>\n", + " <td>0</td>\n", + " <td>NaN</td>\n", + " </tr>\n", + " </tbody>\n", + "</table>\n", + "</div>" + ], + "text/plain": [ + " stud.id name gender age height weight religion \\\n", + "1 833917 Gonzales, Christina Female 19 160 64.8 Muslim \n", + "2 898539 Lozano, T'Hani Female 19 172 73.0 Other \n", + "3 379678 Williams, Hanh Female 22 168 70.6 Protestant \n", + "4 807564 Nem, Denzel Male 19 183 79.7 Other \n", + "5 383291 Powell, Heather Female 21 175 71.4 Catholic \n", + "\n", + " nc.score semester major minor \\\n", + "1 1.91 1st Political Science Social Sciences \n", + "2 1.56 2nd Social Sciences Mathematics and Statistics \n", + "3 1.24 3rd Social Sciences Mathematics and Statistics \n", + "4 1.37 2nd Environmental Sciences Mathematics and Statistics \n", + "5 1.46 1st Environmental Sciences Mathematics and Statistics \n", + "\n", + " score1 score2 online.tutorial graduated salary \n", + "1 NaN NaN 0 0 NaN \n", + "2 NaN NaN 0 0 NaN \n", + "3 45.0 46.0 0 0 NaN \n", + "4 NaN NaN 0 0 NaN \n", + "5 NaN NaN 0 0 NaN " + ] + }, + "execution_count": 3, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "data = pd.read_csv(\"./Daten/students.csv\")\n", + "data.head()" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": { + "tags": [] + }, + "outputs": [ + { + "data": { + "text/plain": [ + "Index(['stud.id', 'name', 'gender', 'age', 'height', 'weight', 'religion',\n", + " 'nc.score', 'semester', 'major', 'minor', 'score1', 'score2',\n", + " 'online.tutorial', 'graduated', 'salary'],\n", + " dtype='object')" + ] + }, + "execution_count": 4, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "data.columns" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": { + "tags": [] + }, + "outputs": [ + { + "data": { + "text/plain": [ + "1 160\n", + "2 172\n", + "3 168\n", + "5 175\n", + "7 156\n", + "Name: height, dtype: int64" + ] + }, + "execution_count": 5, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "female_height = data[data[\"gender\"]== \"Female\"][\"height\"][0:50]\n", + "female_height.head()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Wir betrachten also die Körpergrösse von Frauen, von welcher wir annehmen, dass diese normalverteilt ist. Zur Ueberprüfung dieser Annahme wollen wir den Q-Q-Plot der Körpergrösse der Studentinnen im Datensatz erstellen." + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": { + "tags": [] + }, + "outputs": [ + { + "data": { + "text/plain": [ + "Text(0.5, 1.0, 'Grösse Frauen')" + ] + }, + "execution_count": 6, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": 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", + "text/plain": [ + "<Figure size 640x480 with 1 Axes>" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "st.probplot(female_height,plot=plt)\n", + "plt.title(\"Grösse Frauen\")\n", + "#plt.savefig('qq_students.png', dpi=300)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Aufgrund des QQ-Plots schliessen wir, dass die Körpergrösse von Frauen normalverteilt ist. Wir bezeichnen mit $ X $ die Körpergrösse einer zufällig ausgewählten Studentin, wobei\n", + "$$\n", + "X\n", + "\\sim \\mathcal{N}(\\mu, \\sigma^{2})\n", + "$$\n", + "\n", + "\n", + "Wir wollen nun eine Aussage über $ \\mu $ treffen. Zunächst gehen wir davon aus, dass $ \\sigma $ bekannt ist, sagen wir $ \\sigma=10 $. \n", + "\n", + "Es stellt sich nun die Frage, wie wir die Prior-Verteilung für $ \\mu $ wählen. Eine \n", + "Beta-Verteilung ist für diese Situation nicht passend, da deren Parameterwerte $ \\theta $ nur Werte\n", + "von $ 0 $ bis $ 1 $ annimmt. Viele Verteilungen sind in diesem Fall denkbar. Wir gehen der Einfachheit halber vorläufig von einer gleichförmigen Verteilung aus. Wir gehen hier von grossem Unwissen aus, nämlich dass $ \\mu $ zwischen 100 und 250cm liegen kann , d.h. alle Werte in diesem Bereich können mit der gleichen 'Wahrscheinlichkeit' vorkommen. Natürlich könnten wir hier mehr Vorwissen einfliessen lassen, was wir später auch machen werden." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Als Likelihood-Funktion wählen wir eine Normalverteilungsfunktion mit dem Datensatz `female_height`, der aus 50 Messungen der Körpergrösse von Frauen besteht. Falls $ \\sigma=10 $ und $ x=\\{x_{1},x_{2},\\dots,x_{50} \\} =\\{160,\\ldots, 155\\}$, so lautet die Likelihood-Funktion\n", + "\\begin{align*}\n", + "p(x | \\mu,\\sigma)\n", + "&=\\dfrac{1}{\\sigma\\sqrt{2\\pi}}\\cdot\\exp{\\left(-\\frac{(x_{1}-\\mu)^2}{2\\sigma^2}\\right)}\\cdot\\ldots\\cdot \\dfrac{1}{\\sigma\\sqrt{2\\pi}}\\cdot\\exp{\\left(-\\frac{(x_{50}-\\mu)^2}{2\\sigma^2}\\right)}\\\\\n", + "&=\\dfrac{1}{10\\sqrt{2\\pi}}\\cdot\\exp{\\left(-\\frac{(160-\\mu)^2}{2\\cdot 100}\\right)}\\cdot\\ldots\\cdot \\dfrac{1}{10\\sqrt{2\\pi}}\\cdot\\exp{\\left(-\\frac{(155-\\mu)^2}{2\\cdot 100}\\right)}\\\\\n", + "\\end{align*}" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Diese Likelihood-Funktion betrachten wir nun als abhängig von $ \\mu $ und können nun zusammen mit der Prior-Verteilung die Posterior-Verteilung bestimmen. Dies machen wir nun natürlich mit `pymc3`." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Der Input ist sehr ähnlich wie beim Beta-Prior, aber wir müssen hier 2 Parameter spezifizieren, nämlich $ \\mu $ und $ \\sigma $, da die Likelihood-Funktion von zwei Parametern abhängig ist. Wir wollen zunächst nur einen Parameter, nämlich $ \\mu $, mit MCMC bestimmen." + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": { + "tags": [] + }, + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "Auto-assigning NUTS sampler...\n", + "Initializing NUTS using jitter+adapt_diag...\n", + "Multiprocess sampling (4 chains in 4 jobs)\n", + "NUTS: [μ]\n" + ] + }, + { + "data": { + "text/html": [ + "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\"></pre>\n" + ], + "text/plain": [] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "name": "stderr", + "output_type": "stream", + "text": [ + "Sampling 4 chains for 1_000 tune and 1_000 draw iterations (4_000 + 4_000 draws total) took 1 seconds.\n" + ] + }, + { + "data": { + "text/plain": [ + "<Axes: title={'center': 'μ'}>" + ] + }, + "execution_count": 7, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": 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", + "text/plain": [ + "<Figure size 640x480 with 1 Axes>" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "with pm.Model() as model_g:\n", + " μ = pm.Uniform('μ', lower=100, upper=250)\n", + " σ = 10 \n", + " y = pm.Normal('y', mu=μ, sigma=σ, observed=female_height)\n", + " trace_g = pm.sample()\n", + " \n", + "az.plot_posterior(trace_g)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Wir stellen also fest, dass der Mittelwert der Posterior-Verteilung bei 163cm liegt und dass 94\\% der wahrscheinlichsten $ \\mu $'s im Bereich von 160 bis 165cm liegen.\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Nehmen wir an, eine Zeitung schreibt, dass die durchschnittliche Körpergrösse von Frauen in der Schweiz bei 175cm liegt. Passt diese Angabe zu unseren Daten und zu unserer Prior-Verteilung? " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Männer sind durchschnittlich eher grösser als Frauen. Aber ist dieser Unterschied auch statistisch relevant? Dazu wählen wir 65 Studenten aus und führen dieselbe Untersuchung durch. Wir stellen fest, dass die Körpergrösse dieser 65 Studenten annähernd einer Normalverteilung folgt. " + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": { + "tags": [] + }, + "outputs": [], + "source": [ + "male_height = data[data[\"gender\"]== \"Male\"][\"height\"][0:65]" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Die Berechnung der Posterior-Verteilung der Körpergrösse von Studenten einerseits und die Berechnung der Posterior-Verteilung Körpergrösse von Studentinnen andererseits kann mittels `pymc3`\n", + "beides in einem Schritt durchgeführt werden. \n", + " \n", + "Dazu müssen wir aber zwei $ \\mu$'s spezifizieren, $ \\mu_{1} $ für die Frauen und $ \\mu_{2} $ für die Männer. In Abbildung unten sehen wir die beiden Posterior-Plots." + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": { + "tags": [] + }, + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "Auto-assigning NUTS sampler...\n", + "Initializing NUTS using jitter+adapt_diag...\n", + "Multiprocess sampling (4 chains in 4 jobs)\n", + "NUTS: [μ_1, μ_2]\n" + ] + }, + { + "data": { + "text/html": [ + "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\"></pre>\n" + ], + "text/plain": [] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "name": "stderr", + "output_type": "stream", + "text": [ + "Sampling 4 chains for 1_000 tune and 1_000 draw iterations (4_000 + 4_000 draws total) took 2 seconds.\n" + ] + }, + { + "data": { + "text/plain": [ + "array([<Axes: title={'center': 'μ_1'}>, <Axes: title={'center': 'μ_2'}>],\n", + " dtype=object)" + ] + }, + "execution_count": 9, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": 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", + "text/plain": [ + "<Figure size 1472x552 with 2 Axes>" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "with pm.Model() as model_mul:\n", + " μ_1 = pm.Uniform('μ_1', lower=100, upper=250)\n", + " μ_2 = pm.Uniform('μ_2', lower=100, upper=250)\n", + " σ = 10 \n", + " y_f = pm.Normal('y_f', mu=μ_1, sigma=σ, observed=female_height)\n", + " y_m = pm.Normal('y_m', mu=μ_2, sigma=σ, observed=male_height)\n", + " trace_mul = pm.sample(1000)\n", + "\n", + "az.plot_posterior(trace_mul)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Der 94\\%-HDI von $ \\mu_{1} $ ist $ [160,165] $ und für $ \\mu_{2} $ ist es $ [175,180] $. Das heisst, die wahrscheinlichsten Werte für $ \\mu_{1} $ und $ \\mu_{2} $ überschneiden sich nicht. Wir ziehen daraus den Schluss, dass Männer statistisch relevant grösser sind als Frauen. " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Cohen's $d$ Wert" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Eine gängige Art, die Effektgrösse des Gruppenunterschieds zu quantifizieren, ist mit Hilfe von Cohen's $d$ Wert, welcher wie folgt definiert ist:\n", + "\n", + "\\begin{equation*}\n", + "\\delta=\\frac{\\mu_2 - \\mu_1}{\\sqrt{\\frac{\\sigma_1^2+\\sigma_2^2}{2}}}\n", + "\\end{equation*}\n", + "\n", + "Dieser Ausdruck besagt, dass die Effektgrösse die Differenz zwischen den Gruppenmittelwerten dividiert durch die gepoolte Standardabweichung beider Gruppen ist. Indem wir die gepoolte Standardabweichung nehmen, standardisieren wir die Differenzen der Gruppenmittelwerte. \n", + "\n", + "\n", + "Nehmen wir an, wir haben eine Differenz von 1 zwischen den Gruppenmittelwerten und eine gepoolte Standardabweichung von 0.1, dann ist die Effektgrösse grösser als bei der gleichen Differenz der Gruppenmittelwerte und einer gepoolten Standardabweichung von 10. \n", + "\n", + "Cohen's $d$ Wert kann demzufolge als $z$-Score interpretiert werden. Ein $z$-Score ist die Anzahl Standardabweichungen, die der Gruppenmittelwert der ersten Gruppe vom Gruppenmittelwert der zweiten Gruppe abweicht. \n", + "\n", + "Eine weitere Möglichkeit, eine Kennzahl für die Effektgrösse anzugeben, ist die _\\\"Uberlegenheits-Wahrscheinlichkeit_(englisch _probability of superiority_). Diese ist definiert als die Wahhrscheinlichkeit, dass ein zufällig gewählter Datenpunkt der ersten Gruppe einen grösseren Wert als ein zufällig gewählter Wert der zweiten Gruppe hat. Wenn wir annehmen können, dass die Daten normalverteilt sind, können wir die \\\"Uberlegenheits-Wahrscheinlichkeit mit Hilfe von Cohen's $d$ Wert berechnen:\n", + "\n", + "\\begin{equation*}\n", + "\\text{ps}=\\Phi\\left(\\frac{\\delta}{\\sqrt{2}}\\right)\n", + "\\end{equation*}\n", + "\n", + "wobei $\\text{ps}$ für _probability of superiority_ steht, $\\Phi$ die kumulative Normalverteilung und $\\delta$ Cohen's $d$ Wert bezeichnen.\n", + "\n", + "Im Folgenden Beispiel berechnen wir Cohen's $d$ Wert und die Ueberlegenswahrscheinlichkeit mit Hilfe von `PyMC`." + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": {}, + "outputs": [], + "source": [ + "# Extract posterior samples\n", + "cg_posterior = az.extract(trace_mul)\n", + "\n", + "# Compute mean difference\n", + "means_diff = cg_posterior[\"μ_1\"] - cg_posterior[\"μ_2\"]" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Mit `az.extract()` werden die Werte aus `chain` und `draw` Werten in eine `sample` Koordinate kombiniert. Dies erleichtert weitere Operationen." + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "metadata": {}, + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "The PostScript backend does not support transparency; partially transparent artists will be rendered opaque.\n" + ] + }, + { + "data": { + "image/png": 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", + "text/plain": [ + "<Figure size 700x400 with 1 Axes>" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "\n", + "# Use observed standard deviations (since they were fixed)\n", + "σ_m = male_height.std()\n", + "σ_f = female_height.std()\n", + "\n", + "# Compute pooled standard deviation\n", + "pooled_std = np.sqrt((σ_m**2 + σ_f**2) / 2)\n", + "\n", + "# Compute Cohen's d\n", + "d_cohen = (means_diff / pooled_std).mean().item()\n", + "\n", + "# Compute probability of superiority (PS)\n", + "ps = st.norm.cdf(d_cohen / np.sqrt(2))\n", + "\n", + "# Plot posterior of mean difference\n", + "fig, ax = plt.subplots(figsize=(7, 4))\n", + "az.plot_posterior(means_diff.values, ref_val=0, ax=ax)\n", + "\n", + "# Annotate plot with Cohen's d and probability of superiority\n", + "ax.set_title(\"Posterior of Mean Difference\")\n", + "ax.plot([], [], ' ', label=f\"Cohen's d = {d_cohen:.2f}\\nProb sup = {ps:.2f}\")\n", + "ax.legend(loc=1)\n", + "plt.savefig('cohens_d_students.eps', dpi=300)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Die Wahrscheinlichkeit, dass eine zufällig gewählte Studentin grösser als ein zufällig gewählter Student ist, beträgt 10%. " + ] + } + ], + "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": "3.10.11" + } + }, + "nbformat": 4, + "nbformat_minor": 4 +} diff --git a/notebooks/Normal and t-Distribution/BIND_2_3.ipynb b/notebooks/Normal and t-Distribution/BIND_2_3.ipynb new file mode 100644 index 0000000000000000000000000000000000000000..61c94cbf15b2c64eb09c09aa238b3e9d8091b6f7 --- /dev/null +++ b/notebooks/Normal and t-Distribution/BIND_2_3.ipynb @@ -0,0 +1,384 @@ +{ + "cells": [ + { + "cell_type": "code", + "execution_count": 1, + "metadata": { + "tags": [] + }, + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "WARNING (pytensor.tensor.blas): Using NumPy C-API based implementation for BLAS functions.\n" + ] + } + ], + "source": [ + "import scipy.stats as st\n", + "import matplotlib.pyplot as plt\n", + "import numpy as np\n", + "import pandas as pd\n", + "import warnings \n", + "warnings.filterwarnings(\"ignore\")\n", + "import arviz as az\n", + "import pymc as pm" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Vielleicht haben wir alle aufgrund unserer Erfahrung das Gefühl, dass bei Ehepaaren (oder bei Paaren allgemein) der Ehemann (oder Mann) älter ist als die Ehefrau (oder Frau). Es gibt eine Studie aus Grossbritanien, die diese Behauptung untersucht. Im Datensatz `husband_wife.csv` sind die Daten von 170 Ehepaaren aufgeführt." + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": { + "tags": [] + }, + "outputs": [ + { + "data": { + "text/html": [ + "<div>\n", + "<style scoped>\n", + " .dataframe tbody tr th:only-of-type {\n", + " vertical-align: middle;\n", + " }\n", + "\n", + " .dataframe tbody tr th {\n", + " vertical-align: top;\n", + " }\n", + "\n", + " .dataframe thead th {\n", + " text-align: right;\n", + " }\n", + "</style>\n", + "<table border=\"1\" class=\"dataframe\">\n", + " <thead>\n", + " <tr style=\"text-align: right;\">\n", + " <th></th>\n", + " <th>age.husband</th>\n", + " <th>height.husband</th>\n", + " <th>age.wife</th>\n", + " <th>height.wife</th>\n", + " </tr>\n", + " </thead>\n", + " <tbody>\n", + " <tr>\n", + " <th>0</th>\n", + " <td>49</td>\n", + " <td>180</td>\n", + " <td>43</td>\n", + " <td>159</td>\n", + " </tr>\n", + " <tr>\n", + " <th>1</th>\n", + " <td>25</td>\n", + " <td>184</td>\n", + " <td>28</td>\n", + " <td>156</td>\n", + " </tr>\n", + " <tr>\n", + " <th>2</th>\n", + " <td>40</td>\n", + " <td>165</td>\n", + " <td>30</td>\n", + " <td>162</td>\n", + " </tr>\n", + " <tr>\n", + " <th>3</th>\n", + " <td>52</td>\n", + " <td>177</td>\n", + " <td>57</td>\n", + " <td>154</td>\n", + " </tr>\n", + " <tr>\n", + " <th>4</th>\n", + " <td>58</td>\n", + " <td>161</td>\n", + " <td>52</td>\n", + " <td>142</td>\n", + " </tr>\n", + " </tbody>\n", + "</table>\n", + "</div>" + ], + "text/plain": [ + " age.husband height.husband age.wife height.wife\n", + "0 49 180 43 159\n", + "1 25 184 28 156\n", + "2 40 165 30 162\n", + "3 52 177 57 154\n", + "4 58 161 52 142" + ] + }, + "execution_count": 2, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "data = pd.read_csv(\"./Daten/husband_wife.csv\")\n", + "data.head()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Für jedes Ehepaar gibt es zwei Messungen: das Alter der Ehefrau und das Alter des Ehemannes. Wir interessieren uns für den Altersunterschied. In diesem Fall haben wir ja für jedes Testobjekt, nämlich für jedes Paar, zwei Messgrössen, nämlich das Alter der Frau und das Alter des Mannes. In diesem Fall ist es naheliegend, die `Differenz` des Alters zu betrachten. " + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": { + "tags": [] + }, + "outputs": [ + { + "data": { + "text/plain": [ + "0 6\n", + "1 -3\n", + "2 10\n", + "3 -5\n", + "4 6\n", + "dtype: int64" + ] + }, + "execution_count": 3, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "diff = data[\"age.husband\"] - data[\"age.wife\"]\n", + "diff.head()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Dies hat den Vorteil, dass wir nicht zwei Posterior-Verteilungen betrachten müssen, sondern nur noch eine. \n", + "\n", + "Zuerst wollen wir den Q-Q-Plot der Differenzen in der Abbildung unten betrachten. " + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": { + "tags": [] + }, + "outputs": [ + { + "data": { + "text/plain": [ + "Text(0.5, 1.0, 'Differenz Alter')" + ] + }, + "execution_count": 4, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": 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", + "text/plain": [ + "<Figure size 640x480 with 1 Axes>" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "st.probplot(diff,plot=plt)\n", + "plt.title(\"Differenz Alter\")" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Wir können in diesem Fall von normalverteilten Altersdifferenzen ausgehen, obwohl am unteren und am oberen Ende die Datenpunkte ein bisschen ausreissen. \n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Wir wählen für die Likelihood-Funktion wiederum die Normalverteilung. Als Prior-Verteilung wählen wir auch für diesen Fall eine gleichförmige Verteilung, was unser Unwissen in Bezug auf die Altersdifferenzen ausdrückt. Wir wählen eine Gleichverteilung im Bereich $ [-10, 10] $, d.h., wir gehen also davon aus, dass der mittlere Unterschied im Bereich von $ -10 $ bis $ 10 $ Jahren liegt, wobei alle Werte gleich wahrscheinlich sind. Warum wählen wir auch noch negative Werte von $ \\mu $? Nun wir wissen nicht, ob unsere Erfahrung, dass Ehemänner tendentiell älter sind als ihre Ehefrauen, für alle Ehepaare zutrifft. Es könnte ja sein, dass in _unserem_ Freundeskreis die Ehemänner eher älter sind als die Ehefrauen, wobei dies nicht im Allgemeinen der Fall sein muss. \n", + "\n", + "Da die Standardabweichung schwierig zu schätzen ist, nehmen wir als Standardabweichung die geschätzte Standardabweichung der Daten `diff.std()`. Somit erhalten wir das folgende `pymc3`-Modell." + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": { + "tags": [] + }, + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "Auto-assigning NUTS sampler...\n", + "Initializing NUTS using jitter+adapt_diag...\n", + "Multiprocess sampling (4 chains in 4 jobs)\n", + "NUTS: [μ]\n" + ] + }, + { + "data": { + "text/html": [ + "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\"></pre>\n" + ], + "text/plain": [] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "name": "stderr", + "output_type": "stream", + "text": [ + "Sampling 4 chains for 1_000 tune and 1_000 draw iterations (4_000 + 4_000 draws total) took 3 seconds.\n" + ] + }, + { + "data": { + "text/plain": [ + "<Axes: title={'center': 'μ'}>" + ] + }, + "execution_count": 6, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": 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", + "text/plain": [ + "<Figure size 640x480 with 1 Axes>" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "with pm.Model() as model_paired:\n", + " μ = pm.Uniform('μ', lower=-10, upper=10)\n", + " σ = diff.std()\n", + " y = pm.Normal('y', mu=μ, sigma=σ, observed=diff)\n", + " trace_paired = pm.sample(1000)\n", + "\n", + "az.plot_posterior(trace_paired)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Somit liegt der Mittelwert der Posterior-Verteilung bei $ \\mu=2.2 $ und 94\\% der wahrscheinlichsten Werte für $ \\mu $ liegen im Bereich $ [1.6,2.8] $. \n", + "\n", + "Nun stellt sich noch die Frage, ob es einen statistisch relevanten Unterschied beim Altersunterschied gibt. Nehmen wir einmal an, dass es keinen Altersunterschied gibt, also $ \\mu=0 $. Wie lautet Ihre Test-Entscheidung?" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": {}, + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "Auto-assigning NUTS sampler...\n", + "Initializing NUTS using jitter+adapt_diag...\n", + "Multiprocess sampling (4 chains in 4 jobs)\n", + "NUTS: [μ]\n" + ] + }, + { + "data": { + "text/html": [ + "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\"></pre>\n" + ], + "text/plain": [] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "name": "stderr", + "output_type": "stream", + "text": [ + "Sampling 4 chains for 1_000 tune and 1_000 draw iterations (4_000 + 4_000 draws total) took 1 seconds.\n", + "Sampling: [y, μ]\n", + "The reference value is outside of the posterior. This translate into infinite support for H1, which is most likely an overstatement.\n" + ] + }, + { + "data": { + "text/plain": [ + "({'BF10': 4.730545600529063, 'BF01': 0.21139210662891827},\n", + " <Axes: title={'center': 'The BF_10 is 4.73\\nThe BF_01 is 0.21'}, xlabel='μ', ylabel='Density'>)" + ] + }, + "execution_count": 4, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": 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", + "text/plain": [ + "<Figure size 640x480 with 1 Axes>" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "with pm.Model() as model_h:\n", + " μ = pm.Uniform('μ', lower=-10, upper=10)\n", + " σ = diff.std()\n", + " y = pm.Normal('y', mu=μ, sigma=σ, observed=diff)\n", + " trace_h = pm.sample(1000)\n", + " trace_h.extend(pm.sample_prior_predictive(8000))\n", + "az.plot_bf(trace_h, var_name=\"μ\", ref_val=0)" + ] + } + ], + "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": "3.10.11" + } + }, + "nbformat": 4, + "nbformat_minor": 4 +}