Bayesian Analysis and Model Revision for k’th Order Markov Chains with Unknown k.

Abstract

mass 1 concentrated on the true process, provided that the prior probability measure has full support and the true process is irreducible. Second, I extend this result to the case in which k is unbounded (but finite), which requires that the Bayesian decisionmaker (DM) construct a prior on an infinite-dimensional parameter space. Finally, in an alternative approach to this case, I suppose that the DM considers a succession of models corresponding to larger and larger values of k. Each time the DM revises his model he extends his prior probability measure to the new - and larger - parameter space in a way that is "consistent" with the previous prior, and recomputes his posterior probability measures. I show that, roughly speaking, if the DM does not revise his model “too frequently,” then he will be increasingly confident that the current posterior is increasingly concentrated on the true process. I motivate the procedure of model revision by considerations of bounded rationality.