Bayesian sequential inference for nonlinear multivariate diffusions
Statistics and Computing
Bayesian inference for nonlinear multivariate diffusion models observed with error
Computational Statistics & Data Analysis
Computational methods for complex stochastic systems: a review of some alternatives to MCMC
Statistics and Computing
Inference for non-linear diffusions and jump-diffusions: a Monte Carlo EM approach
ACMIN'12 Proceedings of the 14th international conference on Automatic Control, Modelling & Simulation, and Proceedings of the 11th international conference on Microelectronics, Nanoelectronics, Optoelectronics
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Sparsely sampled diffusion processes, in this paper interpreted as data sampled sparsely in time relative to the time constant, is a challenging statistical problem. Most approximations of the transition kernel are derived under the assumption that data is frequently sampled and these approximations are often severely biased for sparsely sampled data. Monte Carlo methods can be used for this problem as the transition density can be estimated with arbitrary accuracy regardless of the sampling frequency, but this is computationally expensive or even prohibited unless effective variance reduction is applied.The state of art variance reduction technique for diffusion processes is the Durham-Gallant (modified) bridge sampler. Their importance sampler is derived using a linearized, Gaussian approximation of the dynamics, and have proved successful for frequently sampled data. However, the approximation is often not valid for sparsely sampled data.We present a flexible, alternative derivation of the modified bridge sampler for multivariate, discretely observed diffusion models and modify it by taking uncertainty into account. The resulting sampler can be viewed as a combination of the basic sampler and the Durham-Gallant sampler, using the sampler that is most appropriate for the given problem, while still being computationally efficient. Our sampler is providing effective variance reduction for frequently and sparsely sampled data.