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

TL;DR

This paper develops a multilevel Monte Carlo method for Bayesian inference in partially observed stochastic differential equations with jump processes, demonstrating improved computational efficiency in neuroscience models.

Contribution

It adapts the multilevel MCMC approach to SDEs with jumps in neuroscience, showing both theoretical and empirical advantages over single-level methods.

Findings

Multilevel approach reduces computational cost for a given accuracy.

Method effectively handles jump processes in neuroscience models.

Theoretical analysis confirms efficiency gains.

Abstract

In this paper 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 upon the case of neuroscience. The data are assumed to be observed regularly in time and driven by the SDE model with unknown parameters. In practice the SDE may not have an analytically tractable solution and this leads naturally to a time-discretization. We adapt the multilevel Markov chain Monte Carlo method of [11], 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.