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Consistency of Bayesian estimation of a step function

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  • Lian, Heng

Abstract

We study in this paper the consistency of Bayesian estimation of a piecewise constant function defined on [0,1] with observations on a grid, using the method in Barron et al. [1999. The consistency of posterior distributions in nonparametric problems. Ann. Statist. 27, 536-561.] In particular, we show that consistency is achieved if the prior on the number of jumps is a Poisson distribution and the prior puts positive mass on the neighborhood of the true function.

Suggested Citation

  • Lian, Heng, 2007. "Consistency of Bayesian estimation of a step function," Statistics & Probability Letters, Elsevier, vol. 77(1), pages 19-24, January.
    • Handle: RePEc:eee:stapro:v:77:y:2007:i:1:p:19-24
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