Conditioning by rare sources

Details Conditioning by rare sources Conditioning by rare sources

2006-01-03

arxiv.org/abs/math/0601048v2

Mathematics

Statistics Theory

Identical with version 1. Replaced by an error

Scientific paper

In this paper we study the exponential decay of posterior probability of a set of sources and conditioning by rare sources for both uniform and general prior distributions of sources. The decay rate is determined by $L$-divergence and rare sources from a convex, closed set asymptotically conditionally concentrate on an $L$-projection. $L$-projection on a linear family of sources belongs to $\varLambda$-family of distributions. The results parallel those of Large Deviations for Empirical Measures (Sanov's Theorem and Conditional Limit Theorem).

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