Non-parametric Bayesian Inference for Integrals with respect to an Unknown Finite Measure

Author: ERHARDSSON, TORKEL

Source: Scandinavian Journal of Statistics, Volume 35, Number 2, June 2008 , pp. 369-384(16)

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Abstract:

We consider the problem of estimating a collection of integrals with respect to an unknown finite measure μ from noisy observations of some of the integrals. A new method to carry out Bayesian inference for the integrals is proposed. We use a Dirichlet or Gamma process as a prior for μ, and construct an approximation to the posterior distribution of the integrals using the sampling importance resampling algorithm and samples from a new multidimensional version of a Markov chain by Feigin and Tweedie. We prove that the Markov chain is positive Harris recurrent, and that the approximating distribution converges weakly to the posterior as the sample size increases, under a mild integrability condition. Applications to polymer chemistry and mathematical finance are given.

Keywords: Bayesian inference; Dirichlet process; finite measure; Harris recurrence; integral; inverse problem; Markov chain; sampling importance resampling algorithm

Document Type: Research article

DOI: http://dx.doi.org/10.1111/j.1467-9469.2007.00579.x

Affiliations: 1: Department of Mathematics, Linköping University

Publication date: 2008-06-01