Hypothesis testing using Bayesian inferance.

bayesian_update.py

import torch
from torch.distributions.normal import Normal
import matplotlib.pyplot as plt

"""
Using Bayes to estimate the relative probability of 2 Hypotheses given the value of a single data point

Both hypothesis given equal prior probability of being correct
"""

x_axis = torch.linspace(-3.0, 6.0, 50).view(-1, 1)

h = Normal(torch.tensor([1.0, 3.0]), torch.tensor([1.0, 1.0]))
prior = torch.tensor([0.5, 0.5])
eps = torch.finfo(torch.float32).eps

likelyhood = torch.exp(h.log_prob(x_axis))
posterior = likelyhood * prior / ( torch.sum(likelyhood * prior, dim=1, keepdim=True) + eps)

fig, ax = plt.subplots(nrows=2, ncols=1)
ax[0].title.set_text('hypothesis - H')
ax[0].plot(x_axis.squeeze(), torch.exp(h.log_prob(x_axis)))
ax[1].title.set_text('p (H | x)')
ax[1].bar(x_axis.squeeze(), posterior.T[0])
ax[1].bar(x_axis.squeeze(), posterior.T[1], bottom=posterior.T[0])
plt.show()