Tid: 21 november 2011 kl 15.15-16.00.

Föredragshållare: Torkel Erhardsson, Matematiska insitutionen (MAI), Linköpings universitet

Titel: Non-parametric Bayesian inference for integrals with respect to an unknown finite measure

Abstract: We consider the problem of estimating a finite number of integrals with respect to a common unknown finite measure from noisy observations of some of the integrals. A new method to carry out Bayesian inference for the integrals is proposed. We use a Dirich- let or Gamma process as a prior for the measure, and construct an approximation to the posterior distribution of the integrals using the SIR algorithm and samples from a new multidimensional version of a Markov chain introduced 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 number of sam- ples increases, under a mild integrability condition. Applications to polymer chemistry and mathematical finance are given.

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