Bayesian Analysis of Mixture Models with an Unknown Number of Components — an alternative to reversible jump methods
نویسنده
چکیده
Richardson and Green (1997) present 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 (1995). We describe an alternative MCMC method which views the parameters of the model as a (marked) point process, extending methods suggested by Ripley (1977) 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.
منابع مشابه
Bayesian Analysis of Mixture Models with an Unknown Number of Components—an Alternative to Reversible Jump Methods1
Richardson and Green present 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, ext...
متن کاملDynamic Frailty and Change Point Models for Recurrent Events Data
Abstract. We present a Bayesian analysis for recurrent events data using a nonhomogeneous mixed Poisson point process with a dynamic subject-specific frailty function and a dynamic baseline intensity func- tion. The dynamic subject-specific frailty employs a dynamic piecewise constant function with a known pre-specified grid and the baseline in- tensity uses an unknown grid for the piecewise ...
متن کاملOn Bayesian Analysis of Mixtures with an Unknown Number of Components
New methodology for fully Bayesian mixture analysis is developed, making use of reversible jump Markov chain Monte Carlo methods that are capable of jumping between the parameter subspaces corresponding to different numbers of components in the mixture. A sample from the full joint distribution of all unknown variables is thereby generated, and this can be used as a basis for a thorough present...
متن کاملMixture models with a prior on the number of components
A natural Bayesian approach for mixture models with an unknown number of components is to take the usual finite mixture model with symmetric Dirichlet weights, and put a prior on the number of components—that is, to use a mixture of finite mixtures (MFM). The most commonly-used method of inference for MFMs is reversible jump Markov chain Monte Carlo, but it can be nontrivial to design good reve...
متن کاملGibbs Sampling Based Bayesian Analysis of Mixtures with Unknown Number of Components
For mixture models with unknown number of components, Bayesian approaches, as considered by Escobar and West (1995) and Richardson and Green (1997), are reconciled here through a simple Gibbs sampling approach. Specifically, we consider exactly the same direct set up as used by Richardson and Green (1997), but put Dirichlet process prior on the mixture components; the latter has also been used ...
متن کامل