King, Ruth

Elvira Arregui, Victor

Ross, Gordon

Augustin, Nicole

Llewellyn, Mary

Engineering and Physical Sciences Research Council (EPSRC)

2024-08-07T11:42:58Z

2024-08-07T11:42:58Z

2024-08-07

State-space models are widely used to model time series data where the observations depend on a latent process. The latent process consists of a sequence of latent states that evolve according to a specified system process. The observed time series data are then modelled as a function of the latent states via an observation process. Estimating the parameters of a state-space model within a Bayesian framework can be challenging. In this thesis, we consider these challenges and develop efficient Monte Carlo algorithms to aid inference. We propose two classes of method that, as a central theme, leverage approximate hidden Markov models for efficient inference. In the first part of this thesis, we propose that approximate hidden Markov models can be used to design efficient Markov chain Monte Carlo proposal distributions, defined such that the usual theoretical guarantees apply. We discuss how the hidden Markov models are constructed under the proposed approach, the associated generality arising from the tuning parameters, and how these tuning parameters can be chosen efficiently in practice. We demonstrate that this proposed algorithm provides an efficient and robust alternative method for fitting state-space models, even for those that exhibit near-chaotic behaviour. In the second part of this thesis, we develop an approximate hidden Markov model approach to designing efficient particle Markov chain Monte Carlo algorithms. In particular, we propose an approach to particle Gibbs with ancestor sampling that leverages approximate hidden Markov models to combat impoverishment within the sequential Monte Carlo steps of the original algorithm. We additionally propose that fixed approximations to the hidden Markov model can be used to substantially reduce the computational cost of the hidden Markov model and particle Gibbs with ancestor sampling algorithm. We demonstrate the efficiency of this proposed approach in several traditionally challenging examples, focusing on state-space models with regime switching.

https://hdl.handle.net/1842/42066

http://dx.doi.org/10.7488/era/4788

en

The University of Edinburgh

Llewellyn, M., King, R., Elvira, V., Ross, G. (2023). A point mass proposal method for Bayesian state-space model fitting. Statistics and Computing, 33(111). Available at https://doi.org/10.1007/s11222-023-10268-6.

Llewellyn, M., Ross, G., Ryan-Saha, J. (2023). COVID-era forecasting: Google trends and window and model averaging. Annals of Tourism Research, 103:103660. Available at https://doi.org/10.1016/j.annals.2023.103660

Llewellyn, M., King, R., Elvira, V., Ross, G. Grid particle Gibbs with ancestor sampling for efficient state-space model inference

CC BY 4.0 ATTRIBUTION 4.0 INTERNATIONAL Deed

https://creativecommons.org/licenses/by/4.0/

Bayesian state-space model

State-space models

Monte Carlo algorithms

hidden Markov models

Markov chain Monte Carlo proposal distributions

particle Gibbs with ancestor sampling algorithm

Efficient Monte Carlo methods for Bayesian state-space model inference

Thesis or Dissertation

Doctoral

PhD Doctor of Philosophy