Marginal MAP estimation using Markov chain Monte Carlo

Markov chain Monte Carlo (MCMC) methods are powerful simulation-based techniques for sampling from high-dimensional and/or non-standard probability distributions. These methods have recently become very popular in the statistical and signal processing communities as they allow highly complex inference problems in defection and estimation to be addressed. However, MCMC is not currently well adapted to the problem of marginal maximum a posteriori (MMAP) estimation. In this paper, we present a simple and novel MCMC strategy called state-augmentation for marginal estimation (SAME), that allows MMAP estimates to be obtained for Bayesian models. The methodology is very general and we illustrate the simplicity and utility of the approach by examples in MAP parameter estimation for hidden Markov models (HMMs) and for missing data interpolation in autoregressive time series