Markov chain Monte Carlo methods for switching diffusion models

Reversible jump Metropolis-Hastings updating schemes can be used to analyse continuous-time latent models, sometimes known as state space models or hi dden Markov models. We consider models where the observed process X can be represented as a stochastic differential equation and where the latent proc ess D is a continuous-time Markov chain. We develop Markov chain Monte Carl o methods for analysing both Markov and non-Markov versions of these models . As an illustration of how these methods can be used in practice we analys e data from the New York Mercantile Exchange oil market. In addition, we an alyse data generated by a process that has linear and mean reverting states .