Likelihood INference for Discretely Observed Non-linear Diffusions

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 blcked Metropolis-Hastings algorithm, by introducing auxiliary points and by 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.