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Bayesian parameter inference for partially observed stochastic differential equations driven by fractional Brownian motion

Statistics and Computing volume 33, Article number: 19 (2023) Cite this article

Abstract

In this paper we consider Bayesian parameter inference for partially observed fractional Brownian motion models. The approach we follow is to time-discretize the hidden process and then to design Markov chain Monte Carlo (MCMC) algorithms to sample from the posterior density on the parameters given data. We rely on a novel representation of the time discretization, which seeks to sample from an approximation of the posterior and then corrects via importance sampling; the approximation reduces the time (in terms of total observation time T) by \(\mathcal {O}(T)\). This method is extended by using a multilevel MCMC method which can reduce the computational cost to achieve a given mean square error versus using a single time discretization. Our methods are illustrated on simulated and real data.

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Acknowledgements

The authors were supported by KAUST baseline funding.

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Authors and Affiliations

  1. Applied Mathematics and Computational Science Program, Computer, Electrical and Mathematical Sciences and Engineering Division, King Abdullah University of Science and Technology, 23955, Thuwal, Kingdom of Saudi Arabia

    Mohamed Maama & Ajay Jasra

  2. Statistics Program, Computer, Electrical and Mathematical Sciences and Engineering Division, King Abdullah University of Science and Technology, 23955, Thuwal, Kingdom of Saudi Arabia

    Mohamed Maama & Hernando Ombao

Authors
  1. Mohamed Maama
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  2. Ajay Jasra
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  3. Hernando Ombao
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Dr. Mohamed Maama produced all the experiments in the numerical section. Prof: Ajay Jasra wrote the majority of the paper, as well as the structure.

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Correspondence to Mohamed Maama.

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Maama, M., Jasra, A. & Ombao, H. Bayesian parameter inference for partially observed stochastic differential equations driven by fractional Brownian motion. Stat Comput 33, 19 (2023). https://doi.org/10.1007/s11222-022-10193-0

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  • DOI: https://doi.org/10.1007/s11222-022-10193-0

Keywords

  • Fractional Brownian motion
  • Time discretization
  • Multilevel Monte Carlo
  • Markov chain Monte Carlo