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

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  • 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," CUDARE Working Papers 6056, University of California, Berkeley, Department of Agricultural and Resource Economics.
    • Handle: RePEc:ags:ucbecw:6056
    DOI: 10.22004/ag.econ.6056
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    File URL: https://ageconsearch.umn.edu/record/6056/files/wp071048.pdf
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    References listed on IDEAS

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    1. Ganesh, Ayalvadi & O'Connell, Neil, 1999. "An inverse of Sanov's theorem," Statistics & Probability Letters, Elsevier, vol. 42(2), pages 201-206, April.
    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 qt1z012014, Department of Agricultural & Resource Economics, UC Berkeley.
    3. 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.
    4. 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.
    Full references (including those not matched with items on IDEAS)

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