Sankhya: The Indian Journal of Statistics

2006, Volume 68, Pt. 1, 61--89

Mixtures of Conjugate Prior Distributions and Large Deviations for Level Crossing Probabilities

Claudio Macci, University of Rome, Tor Vergata, Italy
Lea Petrella, University of Rome, La Sapienza, Italy

SUMMARY. In this paper we present asymptotic estimates of level crossing probabilities from a Bayesian point of view, based on large deviations. For the Bayesian analysis we choose a finite mixture of conjugate prior distributions to model the uncertainty on the unknown parameters of the two classes of stochastic processes considered: the Brownian motion and the compound Poisson process with upward jumps and negative drift. The estimates of level crossing probabilities are derived as a consequence of large deviation principles for posterior distributions.

AMS (1991) subject classification. Primary 62C10, 60F10.

Key words and phrases. Large deviations, Bayesian asymptotics, mixture of conjugate families, level crossing probabilities.

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