Robust Inference of Dynamic Covariance Using Wishart Processes and Sequential Monte Carlo

Author:

Huijsdens Hester1,Leeftink David1,Geerligs Linda1,Hinne Max1ORCID

Affiliation:

1. Donders Institute for Brain, Cognition and Behaviour, Radboud University Nijmegen, Thomas van Aquinostraat 4, 6525 GD Nijmegen, The Netherlands

Abstract

Several disciplines, such as econometrics, neuroscience, and computational psychology, study the dynamic interactions between variables over time. A Bayesian nonparametric model known as the Wishart process has been shown to be effective in this situation, but its inference remains highly challenging. In this work, we introduce a Sequential Monte Carlo (SMC) sampler for the Wishart process, and show how it compares to conventional inference approaches, namely MCMC and variational inference. Using simulations, we show that SMC sampling results in the most robust estimates and out-of-sample predictions of dynamic covariance. SMC especially outperforms the alternative approaches when using composite covariance functions with correlated parameters. We further demonstrate the practical applicability of our proposed approach on a dataset of clinical depression (n=1), and show how using an accurate representation of the posterior distribution can be used to test for dynamics in covariance.

Funder

Dutch Research Council

Publisher

MDPI AG

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