T Marshall and GO Roberts
Perfect Bayesian Inference for discretely-observed diffusion processes
Date: February, 2008
Abstract: 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 of such a diffusion; we can implement a form of ‘Data Augmentation’ algorithm by alternately imputing the paths between observed points conditional on , and updating for conditional on these imputed paths. Here we look at adapting this data augmentation algorithm to achieve perfect simulation, so that we can draw from the exact posterior distribution of . The algorithm we implement is a form of Read-Once Coupling-From-the-Past; this approach avoids the need to either run the simulation in reverse or retain large amounts of path data in memory. It turns out that there is a very simple Perfect Simulation algorithm that will work for a wide class of diffusions, but its performance deteriorates rapidly with the size of the observed data. Future work will focus on finding algorithms that perform better but remain applicable to a reasonably large class of processes, we suggest some possible approaches.