Gibbs Sampler Algorithm Explained in a Fun and Easy Way!

What is the Gibbs Sampler algorithm and how does it work?

Have you ever wondered how Gibbs Sampler works and why it is used in sampling complex probability distributions?

The Gibbs Sampler algorithm is a Markov Chain Monte Carlo (MCMC) algorithm

The Gibbs Sampler algorithm is a Markov Chain Monte Carlo (MCMC) algorithm that is widely used for sampling from complex probability distributions. It involves initializing variables, iteratively sampling from conditional distributions, and updating the values of the variables.

The algorithm for Gibbs Sampler is quite interesting and fun to understand. It begins by initializing the variables in the model with random values. Then, it repeats a series of steps for a large number of iterations. This involves sampling a new value for each variable from its conditional distribution given the current values of the other variables. After sampling, it updates the values of the variables with the sampled values.

After the iterations, the final values of the variables represent a sample from the joint distribution of the model. The Gibbs Sampler algorithm iteratively samples from conditional distributions to approximate the joint distribution of the variables in the model. By fixing the values of one variable at a time and sampling from its conditional distribution, the algorithm gradually explores the entire joint distribution.

This process of iteratively sampling one variable at a time while fixing the rest allows for efficient sampling from complex probability distributions. It is widely used in fields like Bayesian statistics and machine learning for its effectiveness in sampling from complex distributions.