A New Strategy for Simulating From Mixture Distributions With Applications to Bayesian Model Selection

We present a method of generating random vectors from a distribution having an absolutely continuous component and a discrete component. The method is then extended to more general mixture distributions that arise quite naturally when dealing with nested models within a Bayesian framework. The main idea is to transform the mixture distribution of interest into an absolutely continuous one, in a way that does not require the explicit calculation of the relative weights of the various components of the mixture. For nested models, the proposed method represents a simple alternative to Reversible Jump MCMC schemes. Its distinguishing features are the absence of a proposal step to reduce/increase the dimension of the current space and the fact that in order to assess the convergence of the chain, one can use all the standard tools available for MCMC on a space of fixed dimension KEY WORDS: Bayesian inference; model averaging; Markov chain Monte Carlo. QUADERNO DI DIPARTIMENTO n. 24 - Serie A - Ricerche