Fall 2008 Thursday, October 2   Speaker: Matthew Bognar, Ph.D. Department of Statistics University of Iowa "On Bayesian Inference for Discretely Sampled Diffusion Processes". Abstract: For frequentist inference, the efficacy of the closed-form (CF) likelihood approximation of Ait-Sahalia (2002, 2007) in financial modeling has been widely demonstrated. Bayesian inference, however, requires the use of MCMC, and the CF likelihood can become inaccurate when the parameters are far from the MLE. Due to numerical stability problems, the samplers can therefore become stuck when (typically) in the tails of the posterior distribution. It may be possible to address this problem by using numerical integration to estimate the intractable normalizers in the CF likelihood, but determining the limiting distribution after using such approximations remains an open research question. Auxiliary variables have been used in conjunction with MCMC to address intractable normalizers (see Moller et al. (2006)), but choosing such variables is not trivial. We propose a MCMC algorithm that addresses the intractable normalizers in the CF likelihood which 1) is easy to implement, 2) yields a sampler with the correct limiting distribution, and 3) greatly increases the stability of the sampler compared to using the unnormalized CF likelihood in a standard Metropolis-Hastings algorithm. The efficacy of our approach is demonstrated in a simulation study using the Cox-Ingersoll-Ross (CIR) model. 3:00 Refreshments in 241B Schaeffer Hall 3:30 Talk in 140 Schaeffer Hall

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