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Hypothesentest_IU/Tutorium2_Bayes.ipynb

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{
"cells": [
{
"cell_type": "code",
"execution_count": 12,
"id": "ad2d0815-9390-468e-bf1a-cfcac0411376",
"metadata": {},
"outputs": [],
"source": [
"import numpy as np\n",
"import matplotlib.pyplot as plt\n",
"from scipy.stats import norm, skewnorm"
]
},
{
"cell_type": "markdown",
"id": "686ba9f8-33fe-49f1-820b-861b19e85412",
"metadata": {},
"source": [
"Random variables <br>\n",
"A = Mean height of people (our belief) <br>\n",
"B = Observed heights in the sample (our sample) <br>\n",
"Prior distrubtion P(A) represents the initial beliefs about the parameter before observing any data. <br>\n",
"This distribution reflects your initial belief about the heights of people before considering any new data. The negative skewness indicates that you believe there are more people shorter than 178 cm than taller"
]
},
{
"cell_type": "code",
"execution_count": 9,
"id": "bbaac9a1-8c61-4889-b6f5-ab4fe3bafbc5",
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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",
"text/plain": [
"<Figure size 1000x600 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"# Define the parameters for the prior distribution\n",
"mu_prior = 178\n",
"sigma_prior = 0.5\n",
"skewness_prior = 2.6\n",
"\n",
"# Create a range of x values\n",
"x = np.linspace(175, 185, 1000)\n",
"\n",
"# Calculate the prior distribution with skewness\n",
"prior = skewnorm.pdf(x, skewness_prior, mu_prior, sigma_prior)\n",
"\n",
"# Plot the prior distribution\n",
"plt.figure(figsize=(10, 6))\n",
"plt.plot(x, prior, label='Prior', color='blue')\n",
"plt.xlabel('Height (cm)')\n",
"plt.ylabel('Density')\n",
"plt.title('Prior Distribution with Skewness')\n",
"plt.legend()\n",
"plt.grid(True)\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"id": "26bf7387-13a4-46a0-a3e3-e9b959dd640d",
"metadata": {},
"source": [
"P(B|A) represents the probability of observing the data given a specific parameter value. <br>\n",
"The likelihood is combined with the prior distribution to update our beliefs and form the posterior distribution. <br>\n",
"The likelihood distribution shows how likely it is to observe the given data for different parameter values, the likelihood distribution represents the distribution of the observed data."
]
},
{
"cell_type": "code",
"execution_count": 10,
"id": "a9695aaf-44b0-48fe-a4a8-ab247ab781b0",
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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",
"text/plain": [
"<Figure size 1000x600 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"# Define the parameters for the likelihood distribution\n",
"mu_likelihood = 180\n",
"sigma_likelihood = 0.4\n",
"\n",
"# Create a range of x values\n",
"x = np.linspace(175, 185, 1000)\n",
"\n",
"# Calculate the likelihood distribution\n",
"likelihood = norm.pdf(x, mu_likelihood, sigma_likelihood)\n",
"\n",
"# Plot the likelihood distribution\n",
"plt.figure(figsize=(10, 6))\n",
"plt.plot(x, likelihood, label='Likelihood', color='green')\n",
"plt.xlabel('Height (cm)')\n",
"plt.ylabel('Density')\n",
"plt.title('Likelihood Distribution')\n",
"plt.legend()\n",
"plt.grid(True)\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"id": "ab435d49-644e-4028-a2ba-00da4ad90d51",
"metadata": {},
"source": [
"P(A|B) represents our updated beliefs about the parameter after considering the new data. It is the result of combining the prior distribution and the likelihood distribution. <br>\n",
"The posterior distribution is obtained by combining the prior distribution (with a mean of 178 cm, a standard deviation of 0.5 cm, and a skewness of -0.6) and the likelihood distribution (with a mean of 180 cm and a standard deviation of 0.4 cm). The posterior distribution reflects the updated estimate of the parameter (mean height) after taking into account both the initial beliefs and the new data. <br>\n",
"It is a more accurate estimate of the mean height of people, taking into account both the prior knowledge and the observed data"
]
},
{
"cell_type": "code",
"execution_count": 13,
"id": "df650039-05dd-4c63-ade9-d119114c22de",
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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",
"text/plain": [
"<Figure size 1000x600 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"# Define the parameters for the prior distribution\n",
"mu_prior = 178\n",
"sigma_prior = 0.5\n",
"skewness_prior = -0.6\n",
"\n",
"# Define the parameters for the likelihood distribution\n",
"mu_likelihood = 180\n",
"sigma_likelihood = 0.4\n",
"\n",
"# Create a range of x values\n",
"x = np.linspace(175, 185, 1000)\n",
"\n",
"# Calculate the prior distribution with skewness\n",
"prior = skewnorm.pdf(x, skewness_prior, mu_prior, sigma_prior)\n",
"\n",
"# Calculate the likelihood distribution\n",
"likelihood = norm.pdf(x, mu_likelihood, sigma_likelihood)\n",
"\n",
"# Calculate the posterior distribution using Bayes' theorem\n",
"posterior = prior * likelihood\n",
"posterior /= np.trapezoid(posterior, x) # Normalize the posterior\n",
"\n",
"# Plot the distributions\n",
"plt.figure(figsize=(10, 6))\n",
"plt.plot(x, prior, label='Prior', color='blue')\n",
"plt.plot(x, likelihood, label='Likelihood', color='green')\n",
"plt.plot(x, posterior, label='Posterior', color='red')\n",
"plt.xlabel('Height (cm)')\n",
"plt.ylabel('Density')\n",
"plt.title('Bayesian Inference: Prior, Likelihood, and Posterior Distributions')\n",
"plt.legend()\n",
"plt.grid(True)\n",
"plt.show()"
]
}
],
"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": "3.10.12"
}
},
"nbformat": 4,
"nbformat_minor": 5
}