Andrew Golightly

Bayesian sequential inference for nonlinear multivariate diffusions

We extend recently developed simulation-based sequential algorithms to the Bayesian analysis of partially and discretely observed diffusion processes. Typically, since observations arrive at discrete times, yet the model is formulated in continuous time, it is natural to work with the first order Euler approximation. As the inter-observation times are usually too large to be used as a time step, it is necessary to augment the observed low-frequency data with the introduction of m-1 latent data points in between every pair of observations. Markov chain Monte Carlo (MCMC) methods can then be used to sample the posterior distribution of the latent data and model parameters. Unfortunately, if the amount of augmentation is large, high dependence between parameters and missing data results in arbitrarily slow rates of convergence of basic algorithms such as Gibbs samplers.

We propose a simulation filter, exploiting the diffusion bridge construct of Durham & Gallant (2002), which allows on-line estimation of parameters and state and doesn't break down as m increases. We apply the method to the estimation of parameters governing a simple bivariate log-Gaussian Stochastic Volatility model.