metrics manifesto support code for bayesian analysis

helper_code.py

import pandas as pd
import numpy as np
from scipy.stats import beta, binom



def binomial_beta_mixture(probs: np.array, beta_0: np.array, beta_1: np.array, data: np.array):
    '''
    probs: 
    beta_0: shape of the first beta binomian distribution
    beta_1: shape of the second beta binomial distribution
    data: np.array([success, failure])
    '''
    # implementation of binomial.beta.mix from LearnBayes
    N = len(probs)
    # post.betapar=betapar+outer(rep(1,N),data)
    s = data[0] # success
    f = data[1] # failures
    betapar = np.array([beta_0, beta_1])
    post_betapar = betapar + np.array([data for i in range(0, N)])
    # p=post.betapar[,1]/(post.betapar[,1]+post.betapar[,2])
    p = post_betapar[:, 0] / (post_betapar[:,0]+post_betapar[:,1])
    # dbinom(s,size=s+f,prob=p,log=TRUE)
    component_0 = np.log(binom(s+f, p).pmf(s))    
    # dbeta(p,betapar[,1],betapar[,2],log=TRUE)
    component_1 = np.log(beta(betapar[:,0], betapar[:,1]).pdf(p))
    # dbeta(p,post.betapar[,1],post.betapar[,2],log=TRUE)
    component_2 = np.log(beta(post_betapar[:,0], post_betapar[:,1]).pdf(p))
    mixture_prob = np.exp(component_0 + component_1 - component_2)
    # post.probs=probs*m.prob/sum(probs*m.prob)
    return probs*mixture_prob/np.sum(probs*mixture_prob)