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

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  • TORKEL ERHARDSSON

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.

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  • Torkel Erhardsson, 2008. "Non‐parametric Bayesian Inference for Integrals with respect to an Unknown Finite Measure," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 35(2), pages 369-384, June.
    • Handle: RePEc:bla:scjsta:v:35:y:2008:i:2:p:369-384
    DOI: 10.1111/j.1467-9469.2007.00579.x
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    Cited by:

    1. Dickey, James M. & Jiang, Thomas J. & Kuo, Kun-Lin, 2013. "Distribution of functionals of a Ferguson–Dirichlet process over an n-dimensional ball," Journal of Multivariate Analysis, Elsevier, vol. 120(C), pages 216-225.
    2. Antonio Lijoi & Igor Pruenster, 2009. "Distributional Properties of means of Random Probability Measures," ICER Working Papers - Applied Mathematics Series 22-2009, ICER - International Centre for Economic Research.

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