bayesian_analysis_beta_binomial

# Bayesian Analysis for A/B Experiment with binart goals

import matplotlib
import matplotlib.pyplot as plt

import numpy as np
import scipy as sp
import pandas as pd

def bayesian_analysis(events_a, events_b, successes_a, successes_b, 
                      prior_alpha=1.0, prior_beta=1.0,  N=100000):

    fails_a = events_a - successes_a
    fails_b = events_b - successes_b
    
    a_samples = beta(prior_alpha+successes_a, prior_beta+fails_a, N)
    b_samples = beta(prior_alpha+successes_b, prior_beta+fails_b, N)
    
    a_samples = pd.Series(a_samples)
    b_samples = pd.Series(b_samples)
    
    samples_diff = b_samples - a_samples
    
    samples_diff_median = samples_diff.median()

    fig, axs = plt.subplots(1, 2, figsize=(16,6))

    pd.DataFrame(
        {
            'Posterior A': a_samples,
            'Posterior B': b_samples,
            
        }
    ).plot(
        kind='hist',
        bins=100,
        alpha=0.5,
        ax=axs[0]
    )
    
    samples_diff.plot(
            kind='hist',
            title='Diff B-A',
            bins=100,
            color='Gray',
            ax=axs[1]
    ) 
    
    diff_vline_min, diff_vline_max = axs[1].get_ylim()
    
    axs[1].plot(
        (samples_diff_median, samples_diff_median), 
        (diff_vline_min, diff_vline_max), 
        'Black',
        alpha=0.5,
    )

    axs[1].plot(
        (0, 0), 
        (diff_vline_min, diff_vline_max), 
        'Red',
        alpha=0.5,
    )
    
    print(
        'Credibility of B > A: {}%'.format(
            (
                100 * ((b_samples - a_samples) > 0).mean()
            ).round(2)
        )
    )
    
    print(
        'Credibility of A > B: {}%'.format(
            (
                100 * ((a_samples - b_samples) > 0).mean()
            ).round(2)
        )
    )
    
    print(
        'Differnece (B-A) Median {}%'.format(
            round(100 * samples_diff_median, 2)
        )
    )

    fig.show()
    
    return (a_samples, b_samples)