Work

Unbiased Inference for Discretely Observed Hidden Markov Model Diffusions

Year: 2021

Type: article

Abstract: We develop a Bayesian inference method for diffusions observed discretely and with noise, which is free of discretization bias. Unlike existing unbiased inference methods, our method does not rely on exact simulation techniques. Instead, our method uses standard time-discretized approximations of diffusions, such as the Euler--Maruyama scheme. Our approach is based on particle marginal Metropolis--Hastings, a particle filter, randomized multilevel Monte Carlo, and an importance sampling type correction of approximate Markov chain Monte Carlo. The resulting estimator leads to inference without a bias from the time-discretization as the number of Markov chain iterations increases. We give convergence results and recommend allocations for algorithm inputs. Our method admits a straightforward parallelization and can be computationally efficient. The user-friendly approach is illustrated on three examples, where the underlying diffusion is an Ornstein--Uhlenbeck process, a geometric Brownian motion, and a $2d$ nonreversible Langevin equation.

Source: SIAM/ASA Journal on Uncertainty Quantification

DOI: 10.1137/20m131549x

Authors: Neil K. Chada, Jordan Franks, Ajay Jasra, Kody J. Law, Matti Vihola

Institutions: Newcastle University, University of Manchester, University of Jyväskylä

Language: English

Topic: Markov Chains and Monte Carlo Methods

Subfield: Statistics and Probability

Field: Mathematics

Domain: Physical Sciences

Open Access status: green