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Contributions to the understanding of Bayesian consistency

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  • Antonio Lijoi

    ()

  • Igor Prünster

    ()

  • Stephen G. Walker

    ()

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    Abstract

    Consistency of Bayesian nonparametric procedures has been the focus of a considerable amount of research. Here we deal with strong consistency for Bayesian density estimation. An awkward consequence of inconsistency is pointed out. We investigate reasons for inconsistency and precisely identify the notion of “data tracking”. Specific examples in which this phenomenon can not occur are discussed. When it can happen, we show how and where things can go wrong, in particular the type of sets where the posterior can put mass.

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    File URL: http://servizi.sme.unito.it/icer_repec/RePEc/icr/wp2004/Pruenster13-04.pdf
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    Paper provided by ICER - International Centre for Economic Research in its series ICER Working Papers - Applied Mathematics Series with number 13-2004.

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    Length: 21 pages
    Date of creation: Nov 2004
    Date of revision:
    Handle: RePEc:icr:wpmath:13-2004
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    Keywords: Bayesian consistency; Density estimation; Hellinger distance; Weak neighborhood;

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    Cited by:

    1. Bruce N. Lehmann, 2005. "The Role of Beliefs in Inference for Rational Expectations Models," NBER Working Papers 11758, National Bureau of Economic Research, Inc.
    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. Antonio Lijoi & Igor Prünster & Stephen G. Walker, 2004. "On consistency of nonparametric normal mixtures for Bayesian density estimation," ICER Working Papers - Applied Mathematics Series 23-2004, ICER - International Centre for Economic Research.
    4. Antonio Lijoi & Igor Prünster & Stephen G. Walker, 2004. "On rates of convergence for posterior distributions in infinite–dimensional models," ICER Working Papers - Applied Mathematics Series 24-2004, ICER - International Centre for Economic Research.

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