Add application file

app.py

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+import numpy as np
+import jax.numpy as jnp
+import matplotlib.pyplot as plt
+import numpyro
+import numpyro.distributions as dist
+from numpyro.infer import MCMC, NUTS
+from sklearn.datasets import make_regression
+from jax import random
+import streamlit as st
+
+
+# Define the model
+def linear_regression(X, y, alpha_prior, beta_prior, sigma_prior):
+    alpha = numpyro.sample('alpha', alpha_prior)
+    beta = numpyro.sample('beta', beta_prior)
+    sigma = numpyro.sample('sigma', sigma_prior)
+    mean = alpha + beta * X
+    numpyro.sample('obs', dist.Normal(mean, sigma), obs=y)
+
+
+def run_linear_regression(X, y, alpha_prior, beta_prior, sigma_prior):
+    # Run MCMC
+    rng_key = random.PRNGKey(0)
+    nuts_kernel = NUTS(linear_regression)
+    mcmc = MCMC(nuts_kernel, num_warmup=50, num_samples=1000)
+    mcmc.run(rng_key, jnp.array(X), jnp.array(y), alpha_prior=alpha_prior, beta_prior=beta_prior, sigma_prior=sigma_prior)
+
+    mcmc.print_summary()
+
+    # Get posterior samples
+    samples = mcmc.get_samples()
+
+    # Plot the results
+    fig, ax = plt.subplots(1, 3, figsize=(12, 4))
+    ax[0].hist(samples['alpha'], bins=20, density=True)
+    ax[0].set_title('alpha')
+    ax[1].hist(samples['beta'], bins=20, density=True)
+    ax[1].set_title('beta')
+    ax[2].hist(samples['sigma'], bins=20, density=True)
+    ax[2].set_title('sigma')
+    st.write("The plot of posterior samples is shown below:")
+    st.pyplot(fig)
+    st.write("The mean of alpha is", np.mean(samples['alpha']))
+    st.write("The mean of beta is", np.mean(samples['beta']))
+    st.write("The mean of sigma is", np.mean(samples['sigma']))
+
+    st.write("The plot of predicted line is shown below using mean values of alpha and beta (Xβ+α):")
+    
+
+    fig, ax = plt.subplots(figsize=(8, 6))
+    ax.scatter(X, y, color='blue', alpha=0.5, label='data')
+    light_color = (1.0, 0.5, 0.5, 0.7)
+    for i in range(499):
+        alpha_i = samples['alpha'][i]
+        beta_i = samples['beta'][i]
+        ax.plot(X, alpha_i + beta_i * X, color=light_color)
+    alpha_i = samples['alpha'][498]
+    beta_i = samples['beta'][498]
+    ax.plot(X, alpha_i + beta_i * X, color=light_color,label='MCMC samples')
+    ax.plot(X, np.mean(samples['alpha']) + np.mean(samples['beta']) * X, color='red', label='mean')
+    ax.legend(loc='upper left')
+    st.pyplot(fig)
+
+# User Input
+st.write("# Bayesian Linear Regression")
+
+
+""" Prior: p(α) = N(μ0,Σ0), p(β) = N(μ1,Σ1), p(σ) = N(Σ2)"""
+""" Likelihood: p(y|X,β,α,σ) = N(Xβ+α,σ)"""
+""" Posterior: p(α|X,y) ∝ p(y|X,β,σ)p(α), p(β|X,y) ∝ p(y|X,α,σ)p(β), p(σ|X,y) ∝ p(y|X,β,α)p(σ)"""
+
+
+
+alpha_prior_option = st.selectbox("Choose an option for alpha prior:", ["Normal", "Laplace", "Cauchy"])
+if alpha_prior_option == "Normal":
+    alpha_loc = st.slider("Select a mean value for prior of alpha(α) (μ0)", -10.0, 10.0, 0.0, 0.1)
+    alpha_scale = st.slider("Select a standard deviation value for prior of alpha(α) (Σ0)", 0.01, 10.0, 1.0, 0.1)
+    alpha_prior = dist.Normal(alpha_loc, alpha_scale)
+elif alpha_prior_option == "Laplace":
+    alpha_loc = st.slider("Select a mean value for prior of alpha(α) (μ0)", -10.0, 10.0, 0.0, 0.1)
+    alpha_scale = st.slider("Select a standard deviation value for prior of alpha(α) (Σ0)", 0.01, 10.0, 1.0, 0.1)
+    alpha_prior = dist.Laplace(alpha_loc, alpha_scale)
+elif alpha_prior_option == "Cauchy":
+    alpha_loc = st.slider("Select a mean value for prior of alpha(α) (μ0)", -10.0, 10.0, 0.0, 0.1)
+    alpha_scale = st.slider("Select a standard deviation value for prior of alpha(α) (Σ0)", 0.01, 10.0, 1.0, 0.1)
+    alpha_prior = dist.Cauchy(alpha_loc, alpha_scale)
+
+beta_prior_option = st.selectbox("Choose an option for beta prior:", ["Normal", "Laplace", "Cauchy"])
+if beta_prior_option == "Normal":
+    beta_loc = st.slider("Select a mean value for prior of beta(β) (μ1)", -10.0, 10.0, 0.0, 0.1)
+    beta_scale = st.slider("Select a standard deviation value for prior of beta(β) (Σ1)", 0.01, 10.0, 1.0, 0.1)
+    beta_prior = dist.Normal(beta_loc, beta_scale)
+elif beta_prior_option == "Laplace":
+    beta_loc = st.slider("Select a mean value for prior of beta(β) (μ1)", -10.0, 10.0, 0.0, 0.1)
+    beta_scale = st.slider("Select a standard deviation value for prior of beta(β) (Σ1)", 0.01, 10.0, 1.0, 0.1)
+    beta_prior = dist.Laplace(beta_loc, beta_scale)
+elif beta_prior_option == "Cauchy":
+    beta_loc = st.slider("Select a mean value for prior of beta(β) (μ1)", -10.0, 10.0, 0.0, 0.1)
+    beta_scale = st.slider("Select a standard deviation value for prior of beta(β) (Σ1)", 0.01, 10.0, 1.0, 0.1)
+    beta_prior = dist.Cauchy(beta_loc, beta_scale)
+
+sigma_prior_option = st.selectbox("Choose an option for sigma prior:", ["HalfNormal", "HalfCauchy"])
+if sigma_prior_option == "HalfNormal":
+    sigma_scale = st.slider("Select a scale value for prior of sigma(σ) (Σ2)", 0.01, 10.0, 1.0, 0.1)
+    sigma_prior = dist.HalfNormal(sigma_scale)
+elif sigma_prior_option == "HalfCauchy":
+    sigma_scale = st.slider("Select a scale value for prior of sigma(σ) (Σ2)", 0.01, 10.0, 1.0, 0.1)
+    sigma_prior = dist.HalfCauchy(sigma_scale)
+
+rng_key = random.PRNGKey(0)
+X, y = make_regression(n_samples=50, n_features=1, noise=10.0, random_state=0)
+X = X.reshape(50)
+
+if alpha_prior and beta_prior and sigma_prior:
+    run_linear_regression(X, y, alpha_prior, beta_prior, sigma_prior)