期刊
JOURNAL OF THE ROYAL STATISTICAL SOCIETY SERIES B-STATISTICAL METHODOLOGY
卷 78, 期 2, 页码 343-369出版社
WILEY
DOI: 10.1111/rssb.12118
关键词
Bayesian inference; Coupling; Discretely sampled diffusions; Likelihood inference; Stochastic differential equation; Time reversal
资金
- Mexican Research Council [SNI15945]
- Center for Research in Econometric Analysis of Time Series - Danish National Research Foundation
- University of Copenhagen Programme of Excellence
We propose simple methods for multivariate diffusion bridge simulation, which plays a fundamental role in simulation-based likelihood and Bayesian inference for stochastic differential equations. By a novel application of classical coupling methods, the new approach generalizes a previously proposed simulation method for one-dimensional bridges to the multivariate setting. First a method of simulating approximate, but often very accurate, diffusion bridges is proposed. These approximate bridges are used as proposals for easily implementable Markov chain Monte Carlo algorithms that, apart from a small discretization error, produce exact diffusion bridges. The new method is more generally applicable than previous methods. Another advantage is that the new method works well for diffusion bridges in long intervals because the computational complexity of the method is linear in the length of the interval. In a simulation study the new method performs well, and its usefulness is illustrated by an application to Bayesian estimation for the multivariate hyperbolic diffusion model.
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