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Biometrika 2001 88(3):603-621; doi:10.1093/biomet/88.3.603
© 2001 by Biometrika Trust
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On inference for partially observed nonlinear diffusion models using the Metropolis–Hastings algorithm

G.O. Roberts1 and O.Stramer2

1 Department of Mathematics and Statistics, Lancaster University, Lancaster, LA1 4YF, U.Kg.o.roberts{at}lancaster.ac.uk 2 Department of Statistics and Actuarial Science, University of Iowa, Iowa City, Iowa 52242, U.S.A.stramer{at}stat.uiowa.edu

In this paper, we introduce a new Markov chain Monte Carlo approach to Bayesian analysis of discretely observed diffusion processes. We treat the paths between any two data points as missing data. As such, we show that, because of full dependence between the missing paths and the volatility of the diffusion, the rate of convergence of basic algorithms can be arbitrarily slow 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 Markov chain Monte Carlo algorithms to sample from the posterior-distribution of the transformed missing observations and the parameters of the diffusion. We apply our results to examples involving simulated data and also to Eurodollar short-rate data.

Key Words: Diffusion process; Independence sampler; Markov chain Monte Carlo

Received March 1999. Revised November 2000


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