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Bayesian analysis of mixture models with an unknown number of components – an alternative to reversible jump methods. (English) Zbl 1106.62316
Summary: Richardson and Green presented a method of performing a Bayesian analysis of data from a finite mixture distribution with an unknown number of components. Their method is a Markov Chain Monte Carlo (MCMC) approach, which makes use of the “reversible jump” methodology described by Green. We describe an alternative MCMC method which views the parameters of the model as a (marked) point process, extending methods suggested by Ripley to create a Markov birth-death process with an appropriate stationary distribution. Our method is easy to implement, even in the case of data in more than one dimension, and we illustrate it on both univariate and bivariate data. There appears to be considerable potential for applying these ideas to other contexts, as an alternative to more general reversible jump methods, and we conclude with a brief discussion of how this might be achieved.

62F15Bayesian inference
65C40Computational Markov chains (numerical analysis)
60J80Branching processes
65C60Computational problems in statistics