Bayesian Inference By Simulation in a Stochastic Model From Hematology

Abstract

A particular Markov chain Monte Carlo algorithm is constructed to allow Bayesian inference in a hidden Markov model used in hematology. The algorithm has an outer Gibbsian structure, and incorporates both Metropolis and Hastings updates to move through the space of possible hidden states. While somewhat sophisticated, this algorithm still has problems getting around the infinite-dimensional space of hidden states because of strong correlations between some of the variables. A two-step variant of the Metropolis algorithm is introduced for posterior simulation. Keywords: hidden Markov model, Metropolis algorithm, Gibbs sampler, Hastings algorithm, hematopoiesis 1. A Model Suppose that each of N people in a room is holding a coin--the probability of heads for each coin is p. Independently of one another, each person flips his/her coin at random exponentially-distributed time intervals specified by a rate parameter . Over time, X, the number of facing heads, fluctuates between 0 and N . ..