MCMC for Bayesian uncertainty quantification from time-series data

TL;DR

This paper introduces C++ software for Bayesian uncertainty quantification of Neural Population Models from time-series data using MCMC, incorporating derivative evaluation via finite differences and Algorithmic Differentiation, with applications demonstrated on a harmonic oscillator.

Contribution

The paper presents a modular C++ software framework for derivative-based MCMC in NPMs, integrating both finite difference and Algorithmic Differentiation methods.

Findings

Derivative evaluation methods are compared in MCMC sampling.

Software demonstrates application to a harmonic oscillator example.

Framework is extendable to other scientific domains.

Abstract

Many problems in science and engineering require uncertainty quantification that accounts for observed data. For example, in computational neuroscience, Neural Population Models (NPMs) are mechanistic models that describe brain physiology in a range of different states. Within computational neuroscience there is growing interest in the inverse problem of inferring NPM parameters from recordings such as the EEG (Electroencephalogram). Uncertainty quantification is essential in this application area in order to infer the mechanistic effect of interventions such as anaesthesia. This paper presents C++ software for Bayesian uncertainty quantification in the parameters of NPMs from approximately stationary data using Markov Chain Monte Carlo (MCMC). Modern MCMC methods require first order (and in some cases higher order) derivatives of the posterior density. The software presented offers two distinct methods of evaluating derivatives: finite differences and exact derivatives obtained through Algorithmic Differentiation (AD). For AD, two different implementations are used: the open source Stan Math Library and the commercially licenced dco/c++ tool distributed by NAG (Numerical Algorithms Group). The use of derivative information in MCMC sampling is demonstrated through a simple example, the noise-driven harmonic oscillator. And different methods for computing derivatives are compared. The software is written in a modular object-oriented way such that it can be extended to derivative based MCMC for other scientific domains.