Calculating Bayesian Posterior using Counts

bayes.py

import matplotlib.pyplot as plt
import numpy as np

n_bins = 100


def get_dist(center, scale, bins):
    dist = np.ones(bins)
    s_list = [15, 10, 5, 2]
    power_list = [10, 20, 40, 50]
    for s, pow in zip(s_list, power_list):
        for i in range(int(center - s * scale), int(center + s * scale)):
            if bins <= i or i < 0:
                continue
            dist[i] = pow

    dist[center] = 60
    return dist / dist.sum()


prior = get_dist(center=30, scale=2, bins=n_bins)
likelihood = get_dist(center=50, scale=2, bins=n_bins)


def posterior(p_prior, p_likelihood):
    p_posterior = p_prior * p_likelihood
    print(p_posterior)
    p_posterior = p_posterior / p_posterior.sum()
    return p_posterior


x = np.arange(n_bins)
plt.bar(x, prior, color="b")
plt.bar(x, likelihood, color="r")
plt.bar(x, posterior(prior, likelihood), color="g")
plt.legend(["prior", "likelihood", "posterior"])
plt.show()

result