Constructing a Gibbs sampler for Two component mixture model

Question

The usual two-component Normal mixture model is instructed in these slides http://www2.stat.duke.edu/~rcs46/modern_bayes17/lecturesModernBayes17/lecture-8/08-data-augment.pdf.

We define Latent allocation variables $Z_i$. But how to implement the R code for full conditions of $\mu_0$ and $\mu_1$?

Answer 1

Numerous discussions on the Gibbs sampler for mixtures can be found on this forum:

• Gibbs Sampling for Gaussian Mixtures
• Does Label Switching of Mixture model impact the inference of the whole mixture
• Conditional distribution in this Gaussian Mixture Model
• Bayesian mixture model joint posterior

R packages are available as well

• https://cran.r-project.org/web/packages/sBIC/vignettes/GaussianMixtures.pdf
• https://cran.r-project.org/web/packages/mixtools/vignettes/mixtools.pdf
• https://rdrr.io/cran/ClusterR/man/GMM.html
• https://cran.r-project.org/web/packages/bayesm/index.html

Our book Bayesian Essentials with R (new edition of Bayesian Core) with Jean-Michel Marin contains a whole chapter on mixture models, with R codes available on my webpage. The first edition of our Monte Carlo Statistical Methods with George Casella also enjoys a full chapter on this topic.