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Large Deviations Approach to Bayesian Nonparametric Consistency: the Case of Polya Urn Sampling

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Listed:
  • Grendar, Marian
  • Judge, George G.
  • Niven, R. K.

Abstract

The Bayesian Sanov Theorem (BST) identifies, under both correct and incorrect specification of infinite dimensional model, the points of concentration of the posterior measure. Utilizing this insight in the context of Polya urn sampling, Bayesian nonparametric consistency is established. Polya BST is also used to provide an extension of Maximum Non-parametric Likelihood and Empirical Likelihood methods to the Polya case.

Suggested Citation

  • 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.
    • Handle: RePEc:cdl:agrebk:qt2s97t5km
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    References listed on IDEAS

    as
    1. Grendar, Marian & Judge, George G, 2007. "A Bayesian large deviations probabilistic interpretation and justification of empirical likelihood," CUDARE Working Paper Series 1035, University of California at Berkeley, Department of Agricultural and Resource Economics and Policy.
    2. Grendar, Marian & Judge, George G, 2007. "A Bayesian large deviations probabilistic interpretation and justification of empirical likelihood," Department of Agricultural & Resource Economics, UC Berkeley, Working Paper Series qt3v88z9xf, Department of Agricultural & Resource Economics, UC Berkeley.
    3. Ganesh, Ayalvadi & O'Connell, Neil, 1999. "An inverse of Sanov's theorem," Statistics & Probability Letters, Elsevier, vol. 42(2), pages 201-206, April.
    4. Grendar, Marian & Judge, George G., 2007. "A Bayesian Large Deviations Probabilistic Interpretation and Justification of Empirical Likelihood," Department of Agricultural & Resource Economics, UC Berkeley, Working Paper Series qt1z012014, Department of Agricultural & Resource Economics, UC Berkeley.
    5. Antonio Lijoi & Igor Prünster & Stephen G. Walker, 2004. "Contributions to the understanding of Bayesian consistency," ICER Working Papers - Applied Mathematics Series 13-2004, ICER - International Centre for Economic Research.
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