Simulation of multivariate diffusion bridges

• 成果类型: Article
• 署名作者: Bladt, Mogens; Finch, Samuel; Sorensen, Michael
• 署名单位: Universidad Nacional Autonoma de Mexico; University of Copenhagen
• 刊物名称: JOURNAL OF THE ROYAL STATISTICAL SOCIETY SERIES B-STATISTICAL METHODOLOGY
• ISSN/ISSBN: 1369-7412
• DOI: 10.1111/rssb.12118
• 发表日期: 2016
• 页码: 343-369
• 关键词: maximum-likelihood-estimation; bayesian-inference; time-reversal

摘要

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.