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An inverse of Sanov's theorem

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  • Ganesh, Ayalvadi
  • O'Connell, Neil

Abstract

Let Xk be a sequence of i.i.d. random variables taking values in a finite set, and consider the problem of estimating the law of X1 in a Bayesian framework. We prove that the sequence of posterior distributions satisfies a large deviation principle, and give an explicit expression for the rate function. As an application, we obtain an asymptotic formula for the predictive probability of ruin in the classical gambler's ruin problem.

Suggested Citation

  • Ganesh, Ayalvadi & O'Connell, Neil, 1999. "An inverse of Sanov's theorem," Statistics & Probability Letters, Elsevier, vol. 42(2), pages 201-206, April.
    • Handle: RePEc:eee:stapro:v:42:y:1999:i:2:p:201-206
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    References listed on IDEAS

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    1. James Fu & Robert Kass, 1988. "The exponential rates of convergence of posterior distributions," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 40(4), pages 683-691, December.
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    Cited by:

    1. Grendar, Marian & Judge, George G. & Niven, R. K., 2007. "Large Deviations Approach to Bayesian Nonparametric Consistency: the Case of Polya Urn Sampling," Department of Agricultural & Resource Economics, UC Berkeley, Working Paper Series qt2s97t5km, Department of Agricultural & Resource Economics, UC Berkeley.
    2. Grendar, Marian & Judge, George G. & Niven, R. K., 2007. "Large Deviations Approach to Bayesian Nonparametric Consistency: the Case of Polya Urn Sampling," Department of Agricultural & Resource Economics, UC Berkeley, Working Paper Series qt2s97t5km, Department of Agricultural & Resource Economics, UC Berkeley.
    3. Macci, Claudio, 2011. "Large deviations for estimators of unknown probabilities, with applications in risk theory," Statistics & Probability Letters, Elsevier, vol. 81(1), pages 16-24, January.

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    Keywords

    Large deviations Bayes asymptotics;

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