Covariate-guided Bayesian mixture model for multivariate time series

TL;DR

This paper introduces a Bayesian mixture model incorporating covariates to cluster multivariate time series data from brain imaging, enabling the identification of distinct brain activity patterns linked to covariates.

Contribution

It presents a novel covariate-guided Bayesian mixture model for multivariate time series, with a fully Bayesian inference framework and component number selection based on deviance information criterion.

Findings

Identified distinct brain activity patterns in fNIRS data.

Revealed associations between brain activity patterns and covariates.

Demonstrated improved clustering performance over existing methods.

Abstract

With rapid development of techniques to measure brain activity and structure, statistical methods for analyzing modern brain-imaging play an important role in the advancement of science. Imaging data that measure brain function are usually multivariate time series and are heterogeneous across both imaging sources and subjects, which lead to various statistical and computational challenges. In this paper, we propose a group-based method to cluster a collection of multivariate time series via a Bayesian mixture of smoothing splines. Our method assumes each multivariate time series is a mixture of multiple components with different mixing weights. Time-independent covariates are assumed to be associated with the mixture components and are incorporated via logistic weights of a mixture-of-experts model. We formulate this approach under a fully Bayesian framework using Gibbs sampling where the number of components is selected based on a deviance information criterion. The proposed method is compared to existing methods via simulation studies and is applied to a study on functional near-infrared spectroscopy (fNIRS), which aims to understand infant emotional reactivity and recovery from stress. The results reveal distinct patterns of brain activity, as well as associations between these patterns and selected covariates.