Some novel Monte Carlo algorithms for challenging inference problems

• Main Author: Marshall, Tristan Roy Gray
• Published: Lancaster University 2009
• Subjects: 578.282
• Online Access: http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.556695

This work consists of two separate parts. In the first part we extend the work on exact simulation of diffusions introduced in [9]. The authors in that paper introduced a methodology for simulating a diffusion process and for performing parametric inference for a partially observed diffusion. In particular they demonstrated how to perform Bayesian inference for a parameter θ of such a diffusion; it is possible to implement a Gibbs Sampler that alternately imputes the paths between observed points conditionally on θ, and updating for θ conditionally on the imputed paths. , This algorithm simulates values (θn)n≥l whose distribution converges to the true posterior in the n→t ∞ limit; we extend their algorithm to simulate exact samples from the posterior within a finite time - so-called perfect simulation. In the second part we consider a class of adaptive MCMC algorithms using a Langevin-type proposal density. We state and prove regularity conditions for the convergence of these algorithms. In addition to these theoretical results we introduce a number of methodological innovations that can be applied much more generally. We assess the performance of these algorithms with simulation studies, including an example of the statistical analysis of a point process driven by a latent log-Gaussian Cox process.