Multilevel Monte Carlo for a class of Partially Observed Processes in Neuroscience

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B9 L2 H2

In this talk, we consider Bayesian parameter inference associated to a class of partially observed stochastic differential equations (SDE) driven by jump processes. Such type of models can be routinely found in applications, of which we focus on the case of neuroscience.

Abstract

In this talk, we consider Bayesian parameter inference associated to a class of partially observed stochastic differential equations (SDE) driven by jump processes. Such type of models can be routinely found in applications, of which we focus on the case of neuroscience. The data are assumed to be observed regularly in time and driven by the SDE model with unknown parameters.  We adopt the multilevel Markov chain Monte Carlo method of (reference is in the main article), which works with a hierarchy of time discretizations, and show empirically and theoretically that this is preferable to using one single-time discretization. The improvement is in terms of the computational cost needed to obtain a pre-specified numerical error. Our approach is illustrated on models that are found in neuroscience. This is a joint work with Ajay Jasra (KAUST) and Kengo Kamatani (ISM, JAPON).

Brief Biography

Mohamed Maama joined KAUST in December 2021 as a Postdoctoral Research Fellow in the Computational Probability group under the supervision of Prof. Ajay Jasra. He earned his Ph.D. in Applied Mathematics at Normandie Université, France, in 2020.  His research interests encompass both Computational and Applied Mathematics as well as Statistics.