*Tid:* **21 november 2011 kl 15.15-16.00.**
**Seminarierummet 3721**, Institutionen för
matematik, KTH, Lindstedts väg 25, plan 7.
Karta!
*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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