# Inferring GMM parameters with Gibbs Sampling

On my book, "Machine Learning A Probabilistic Approach". It's stated that is straightforward to derive a Gibbs sampling algorithm to fit a mixture model, especially if we use conjugate priors.

So straightforward that book gives an example of fitting Mixture Gaussian without actually giving the resulting fitting algorithm.

Here the example:

My question is: once I have all the full conditionals of the discrete indicators, mixing weight, means and covariance, how shold I proceed for actually fitting my data? What is the algorithm that I should follow?

• You should first read the section on Gibbs sampling. – Xi'an Jan 11 at 13:29
• I've read it but I can just hunch the prototype of the algorithm, do I need to sample in turn from equation 24.10, 24.11, 24.12, 24.17, using the new samples values each time? – Tommaso Bendinelli Jan 11 at 14:03

If I learned this right, you use the MCMC estimates essentially as replacement for the M step, in an EM like process.

The idea is simple: if we cannot solve the maximum likelihood problem exactly, we use anumeric approximation instead.