Large Deviations for Mixtures
J. D. Biggins, The University of Sheffield, UK
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
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