This Python script demonstrates the application of the Metropolis-Hastings algorithm, a Markov chain Monte Carlo (MCMC) method, to perform Bayesian inference on company personnel data.
y_i are random identically distributed and independent variables, with mean mu and variance 1. Our prior distribution on mu is the t-distribution with location 0, scale parameter 1, and degrees of freedom 1. The goal is to sample from the posterior distribution of the first using the Metropolis-Hastings algorithm.
Key Functions:
- log_g_fun(mu, n, y_bar): Computes the log posterior distribution for mu
- metropolis_hastings(n, y_bar, n_iter, mu_init, cand_std): Implements the Metropolis-Hastings algorithm. Returns posterior samples and acceptance ratio.
Convergence to this distribution for the validity of the samples drawn. Our init mean was far from the real in order to test how many samples are needed to get close.
Density comparisons prior vs posterior: the posterior shortens the true mean of the data.
