Unbiased Inference for Discretely observed Hidden Markov Model Diffusions

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• Neil Chada (King Abdullah University of Science and Technology)
• Tuesday 06 July 2021, 15:00-16:00
• https://bham-ac-uk.zoom.us/j/3900445385?pwd=Mk1LSmRiUk5STEJMWVl0bE82NTM1QT09.

If you have a question about this talk, please contact Hong Duong.

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

This talk is part of the Data Science and Computational Statistics Seminar series.

This talk is included in these lists:

• Analysis Seminar
• Data Science and Computational Statistics Seminar
• School of Mathematics Events
• https://bham-ac-uk.zoom.us/j/3900445385?pwd=Mk1LSmRiUk5STEJMWVl0bE82NTM1QT09

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