Bayesian Analysis and Model Revision for Kã¢Â¬Â"Th Order Markov Chains with Unknown K.
36 Pages Posted: 9 Oct 2008
Date Written: October 2002
mass 1 concentrated on the true process, provided that the prior probability measurehas full support and the true process is irreducible. Second, I extend this result to thecase in which k is unbounded (but finite), which requires that the Bayesian decisionmaker(DM) construct a prior on an infinite-dimensional parameter space. Finally, inan alternative approach to this case, I suppose that the DM considers a succession ofmodels corresponding to larger and larger values of k. Each time the DM revises hismodel he extends his prior probability measure to the new - and larger - parameterspace in a way that is "consistent" with the previous prior, and recomputes his posteriorprobability measures. I show that, roughly speaking, if the DM does not revisehis model Ã¢Â¬ÂStoo frequently,Ã¢Â¬Â? then he will be increasingly confident that the currentposterior is increasingly concentrated on the true process. I motivate the procedureof model revision by considerations of bounded rationality.
Keywords: Bayesian analysis, model revision, bounded rationality
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