Simple formula to find Bayesian A/B test confidence

bayesian_ab_test.py

import math

def calc_ab(conversion_a, interaction_a, conversion_b, interaction_b):
    # more generic function which takes conversions and interactions. Calculates failures internally
    # total is the confidence that b is doing better than a
    alpha_a = conversion_a + 1
    alpha_b = conversion_b + 1
    beta_a = interaction_a - conversion_a + 1
    beta_b = interaction_b - conversion_b + 1
    total = 0.0
    for i in range(alpha_b): # loop till alphab - 1
        num = math.lgamma(alpha_a+i) + math.lgamma(beta_a+beta_b) + math.lgamma(1+i+beta_b) + math.lgamma(alpha_a+beta_a)
        den = math.log(beta_b+i) + math.lgamma(alpha_a+i+beta_a+beta_b) + math.lgamma(1+i) + math.lgamma(beta_b) + math.lgamma(alpha_a) + math.lgamma(beta_a)
        total += math.exp(num - den)
    return total