Beta Distribution Applet - Interactive Beta Distribution Plot

If you'd like to reproduce this interactive plot in Python with PyTorch, here is the code:

import numpy as np
import matplotlib.pyplot as plt
import torch
from torch.distributions import Beta
from torch.distributions.kl import kl_divergence
from ipywidgets import interactive, FloatSlider, Layout
from IPython.display import display

def plot_beta_interactive(a=1.0, b=1.0, a2=2.0, b2=2.0):
	# Create Beta distributions
	distribution1 = Beta(torch.tensor(a), torch.tensor(b))
	distribution2 = Beta(torch.tensor(a2), torch.tensor(b2))
	
	# Create x values
	x = torch.linspace(0, 1, 1000)
	
	# Calculate PDFs
	pdf1 = torch.exp(distribution1.log_prob(x))
	pdf2 = torch.exp(distribution2.log_prob(x))
	
	# Convert to numpy
	x_np = x.numpy()
	pdf1_np = pdf1.numpy()
	pdf2_np = pdf2.numpy()
	
	# Calculate KL divergence
	kl = kl_divergence(distribution1, distribution2).item()
	
	# Create the plot
	plt.figure(figsize=(10, 6))
	plt.plot(x_np, pdf1_np, label=f'Beta(α={{a:.2f}}, β={{b:.2f}})')
	plt.fill_between(x_np, pdf1_np, alpha=0.3)
	plt.plot(x_np, pdf2_np, label=f'Beta(α={{a2:.2f}}, β={{b2:.2f}})')
	plt.fill_between(x_np, pdf2_np, alpha=0.3)
	
	# Add KL divergence to the plot
	plt.text(0.4, 0.85, f'KL(P||Q) = {{kl:.4f}}', transform=plt.gca().transAxes, 
			 verticalalignment='top', bbox=dict(boxstyle='round', facecolor='white', alpha=0.8))
	
	plt.xlabel('x')
	plt.ylabel('Probability Density')
	plt.title(f'Beta Distributions: (α={{a:.2f}}, β={{b:.2f}}) and (α={{a2:.2f}}, β={{b2:.2f}})')
	plt.legend()
	plt.grid(True, alpha=0.3)
	plt.show()

# Create interactive plot
def create_interactive_beta_plot():
	slider_layout = Layout(width='500px')
	
	interactive_plot = interactive(
		plot_beta_interactive,
		a=FloatSlider(min=0.001, max=100, step=0.001, value=1, description='a:', layout=slider_layout),
		b=FloatSlider(min=0.001, max=100, step=0.001, value=1, description='b:', layout=slider_layout),
		a2=FloatSlider(min=0.001, max=100, step=0.001, value=2, description='a2:', layout=slider_layout),
		b2=FloatSlider(min=0.001, max=100, step=0.001, value=2, description='b2:', layout=slider_layout)
	)
	
	display(interactive_plot)

# Finally, run:
create_interactive_beta_plot()