Bayesian Parameter Inference for Partially Observed SDEs driven by Fractional Brownian Motion

Mohamed Maama; Ajay Jasra; Hernando Ombao

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arXiv · 2211.00296

Bayesian Parameter Inference for Partially Observed SDEs driven by Fractional Brownian Motion

Mohamed Maama·Ajay Jasra·Hernando Ombao

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Abstract

In this paper we consider Bayesian parameter inference for partially observed fractional Brownian motion (fBM) 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 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 (MSE) versus using a single time discretization. Our methods are illustrated on simulated and real data.

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BibTeX RIS

Mohamed Maama, Ajay Jasra, Hernando Ombao. 2022-11-01. Bayesian Parameter Inference for Partially Observed SDEs driven by Fractional Brownian Motion. https://arxiv.org/abs/2211.00296

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