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Variational Bayes and a problem of reliable communication: II. Infinite systems

Newton, NJ and Mitter, SK (2012) 'Variational Bayes and a problem of reliable communication: II. Infinite systems.' Journal of Statistical Mechanics: Theory and Experiment, 2012 (11). ISSN 1742-5468

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We consider a family of estimation problems not admitting conventional analysis because of singularity and measurability issues. We define posterior distributions for the family by a variational technique analogous to that used to define Gibbs measures in statistical mechanics. The family of estimation problems, which arise in the asymptotic analysis of error-control codes, is parametrized by a code rate, R∈(0,∞); this is shown to be analogous to the absolute temperature of statistical mechanics. The family undergoes an (Ehrenfest) first-order phase transition at a critical code rate C (the channel capacity), where there is a convex set of posterior distributions. At all other code rates, there is only one posterior distribution; if R < C, this is the Dirac measure located at the source sequence, whereas if R > C it has infinite support. In a result reflecting the Dobrushin construction, we show that these posterior distributions are asymptotically consistent with those of families of finite-sequence error-control codes. © 2012 IOP Publishing Ltd and SISSA Medialab srl.

Item Type: Article
Subjects: Q Science > QA Mathematics
Q Science > QA Mathematics > QA75 Electronic computers. Computer science
Q Science > QC Physics
Divisions: Faculty of Science and Health > Computer Science and Electronic Engineering, School of
Depositing User: Jim Jamieson
Date Deposited: 05 Mar 2013 16:28
Last Modified: 23 Jan 2019 05:15

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