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2004 Large Deviations for Mixtures
J. D. Biggins
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Electron. Commun. Probab. 9: 60-71 (2004). DOI: 10.1214/ECP.v9-1106

Abstract

The results discussed here are most easily described in words using Bayesian terminology. For each $n$, there are probability distributions for the data conditional on a parameter, and there is also a prior distribution for the parameter. Integrating out, using the prior, gives the (unconditional) distribution for the data, for each $n$. The question considered here is when large deviation principles for the conditional distributions and for the prior distributions imply a large deviation principle for the unconditional distributions. Chaganty (1997) also considered this question, but under stronger assumptions. The treatment here follows that of Dinwoodie and Zabell (1992) who, motivated by exchangeability, considered the case where the prior does not vary with $n$.

Citation

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J. D. Biggins. "Large Deviations for Mixtures." Electron. Commun. Probab. 9 60 - 71, 2004. https://doi.org/10.1214/ECP.v9-1106

Information

Accepted: 9 June 2004; Published: 2004
First available in Project Euclid: 26 May 2016

zbMATH: 1060.60026
MathSciNet: MR2081460
Digital Object Identifier: 10.1214/ECP.v9-1106

Subjects:
Primary: 60F10

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