Two-Sample Testing for Multivariate Cross-Correlation Functions with Applications to Gut-Brain Reward Learning

2026-04-05

AI Summary

This study addresses the challenge of testing differences in dynamic dependence structures of multivariate cross-correlation functions across experimental conditions by introducing, for the first time, a functional data analysis framework to this domain. Methodologically, cross-correlation functions are treated as multivariate functional data, and global test statistics—both integral- and supremum-type—are constructed based on pointwise Hotelling’s T² statistics to perform two-sample hypothesis tests on mean functions, thereby enabling simultaneous detection of both global and local discrepancies. In application, the proposed approach reveals significant differences in dopamine–movement coupling across brain regions and between sexes under ad libitum feeding conditions, while perfusion experiments exhibit more specific effects, underscoring the method’s practical utility and innovation in neuroscience data analysis.

Abstract

Cross-correlation functions (CCFs) are classical tools for studying lead-lag relationships between paired time series, but they are most often used descriptively rather than inferentially. Motivated by mouse experiments on gut-brain interactions in reward learning, we carry out a two-sample hypothesis test for formal statistical inference on collections of subject-specific CCF curves. In our application, each experimental session yields two related CCFs describing the temporal association of dopamine activity with locomotor velocity and acceleration, which leads naturally to a multivariate functional data formulation. We treat each empirical CCF as a functional observation indexed by lag and test equality of mean multivariate CCF functions across groups using integrated and maximum-type global statistics, \(F_{\mathrm{int}}\) and \(F_{\max}\), constructed from pointwise Hotelling \(T^2\) statistics. The integrated test targets broad differences across the lag domain, whereas the maximum test is sensitive to local differences. Applied to free-feeding and intragastric infusion datasets, the proposed methods detect substantial differences in dopamine-locomotion coupling across brain region and biological sex in the free-feeding experiment, with more selective effects in the infusion setting. The proposed framework provides a flexible and rigorous FDA-based approach for comparing dynamic dependence structures across experimental conditions.

Problem

• two-sample testing
• multivariate cross-correlation functions
• functional data analysis
• dynamic dependence
• hypothesis testing

Innovation

• multivariate functional data analysis
• cross-correlation function
• two-sample testing
• Hotelling T² statistic
• dynamic dependence