Simulation of multivariate diffusion bridges

TY - JOUR

T1 - Simulation of multivariate diffusion bridges

AU - Bladt, Mogens

AU - Finch, Samuel Thomas John

AU - Sørensen, Michael

PY - 2016/3/1

Y1 - 2016/3/1

N2 - 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.

AB - 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.

U2 - 10.1111/rssb.12118

DO - 10.1111/rssb.12118

M3 - Journal article

SN - 1369-7412

VL - 78

SP - 343

EP - 369

JO - Journal of the Royal Statistical Society, Series B (Statistical Methodology)

JF - Journal of the Royal Statistical Society, Series B (Statistical Methodology)

IS - 2

ER -