A Generalization of B. S. Clarke and A. R. Barron's Asymptotics of Bayes Codes for FSMX Sources

Masayuki GOTOH  Toshiyasu MATSUSHIMA  Shigeichi HIRASAWA  

IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E81-A    No.10    pp.2123-2132
Publication Date: 1998/10/25
Online ISSN: 
Print ISSN: 0916-8508
Type of Manuscript: Special Section PAPER (Special Section on Information Theory and Its Applications)
Category: Source Coding
Bayes code,  source coding,  universal coding,  universal modeling,  

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We shall generalize B. S. Clarke and A. R. Barron 's analysis of the Bayes method for the FSMX sources. The FSMX source considered here is specified by the set of all states and its parameter value. At first, we show the asymptotic codelengths of individual sequences of the Bayes codes for the FSMX sources. Secondly, we show the asymptotic expected codelengths. The Bayesian posterior density and the maximum likelihood estimator satisfy asymptotic normality for the finite ergodic Markov source, and this is the key of our analysis.