Bayesian inference for irreducible diffusion processes using the pseudo-marginal approach

By Osnat Stramer, Ia Matthew Bognar. 2011

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In this article we examine two relatively new MCMC methods which allow for Bayesian inference in diffusion models. First, the Monte Carlo within Metropolis (MCWM) algorithm (O’Neil, Balding, Becker, Serola and Mollison, 2000) uses an importance sampling approximation for the likelihood and yields a limiting stationary distribution that can be made arbitrarily “close” to the posterior distribution (MCWM is not a standard Metropolis-Hastings algorithm, however). The second method, described in Beaumont (2003) and generalized in Andrieu and Roberts (2009), introduces auxiliary variables and utilizes a standard Metropolis-Hastings algorithm on the enlarged space; this method preserves the original posterior distribution. When applied to diffusion models, this approach can be viewed as a generalization of the popular data augmentation schemes that sample jointly from the missing paths and the parameters of the diffusion volatility. We show that increasing the number of auxiliary variables dramatically increases the acceptance rates in the MCMC algorithm (compared to basic data augmentation schemes), allowing for rapid convergence and mixing. The efficacy of ourapproach is demonstrated in a simulation study of the Cox-Ingersoll-Ross (CIR) and Heston models, and is applied to two well known datasets.

Subfields: Artificial Intelligence, Finance, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/2f4a1332b46875e5ac1abe1db34ddc95d9fae180