LIKELIHOOD INFERENCE FOR DISCRETELY OBSERVED NON-LINEAR DIFFUSIONS

Ola Elerian

Nuffield College

Siddhartha Chib

Washington University

and

Neil Shephard

Nuffield College

 

August 1998

 

Abstract

This paper is concerned with the Bayesian estimation of non-linear stochastic differential equations when only discrete observations are available. The estimation is carried out using a tuned MCMC method, in particular a blocked Metropolis-Hastings algorithm, by introducing auxiliary points and using the Euler-Maruyama discretisation scheme. Techniques for computing the likelihood function, the marginal likelihood and diagnostic measures (all based on the MCMC output) are presented. Examples using simulated and real date are presented and discussed in detail.