Create a Monte Carlo simulation Gibbs sampler in Python

A Monte Carlo Gibbs sampler is a powerful Markov Chain Monte Carlo (MCMC) technique used to sample from complex, multidimensional probability distributions.

Monte Carlo methods involve random sampling to estimate numerical results am=nd are used in various fields to include statistical physics, finance, and engineering.

Gibbs sampling is a special type of MCMC method where the sampling is accomplished by iteratively sampling from the conditional distributions of each variable in turn, given the current values of the other variables.

Gibbs sampling works by:-

1. Start with the initial values of each variable in the distribution.
2. Sequentially sample from conditional distribution of each variable. For example, in a two variable distribution being X and Y, sample X given Y in P(X|Y) and sample Y given X in P(Y|X).
3. After a number of iterations, called the burn-in period, the samples converge to the target joint distribution.

The applications that Gibbs sampling is used in are:-

1. Bayesian inference
2. Statistical physics
3. Machine learning