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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.
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    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.

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    Bibliographic Info

    Paper provided by Department of Agricultural & Resource Economics, UC Berkeley in its series Department of Agricultural & Resource Economics, UC Berkeley, Working Paper Series with number qt2s97t5km.

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    Date of creation: 21 Sep 2007
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    Handle: RePEc:cdl:agrebk:qt2s97t5km

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    Keywords: Polya L-divergence; Bayesian Maximum (A Posteriori) Probability method; Maximum Non-parametric Likelihood method; Empirical Likelihood method;

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    1. Antonio Lijoi & Igor PrĂ¼nster & 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.
    2. Ganesh, Ayalvadi & O'Connell, Neil, 1999. "An inverse of Sanov's theorem," Statistics & Probability Letters, Elsevier, vol. 42(2), pages 201-206, April.
    3. Mittelhammer,Ron C. & Judge,George G. & Miller,Douglas J., 2000. "Econometric Foundations Pack with CD-ROM," Cambridge Books, Cambridge University Press, number 9780521623940, April.
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