Mixture models with an unknown number of components via a new posterior split–merge MCMC algorithm

In this paper we introduce a Bayesian analysis for mixture models with an unknown number of components via a new posterior split–merge MCMC algorithm. Our strategy for splitting is based on data in which allocation probabilities are calculated based on posterior distribution from the previously allocated observations. This procedure is easy to be implemented and determines a quick split proposal. The acceptance probability for split–merge movements are calculated according to metropolised Carlin and Chib’s procedure. The performance of the proposed algorithm is verified using artificial datasets as well as two real datasets. The first real data set is the benchmark galaxy data, while the second is the publicly available data set on Escherichia coli bacterium.