On inference for partially observed nonlinear diffusion models using the Metropolis-Hastings algorithm

In this paper, we introduce a new Markov chain Monte Carlo approach to Baye sian analysis of discretely observed diffusion processes. We treat the path s between any two data points as missing data. As such, we show that, becau se of full dependence between the missing paths and the volatility of the d iffusion, the rate of convergence of basic algorithms can be arbitrarily sl ow if the amount of the augmentation is large. We offer a transformation of the diffusion which breaks down dependency between the transformed missing paths and the volatility of the diffusion. We then propose two efficient M arkov chain Monte Carlo algorithms to sample from the posterior-distributio n of the transformed missing observations and the parameters of the diffusi on. We apply our results to examples involving simulated data and also to E urodollar short-rate data.