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

Full text not available from this repository.## Abstract

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 |
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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: | 11 Jan 2018 16:15 |

URI: | http://repository.essex.ac.uk/id/eprint/5537 |

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