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| Main Authors: | , , , |
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| Format: | Preprint |
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2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2604.04156 |
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| _version_ | 1866910105203638272 |
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| author | Ray, Bhaskar Bùi, Tùng Howe, William Matthew Sengupta, Srijan |
| author_facet | Ray, Bhaskar Bùi, Tùng Howe, William Matthew Sengupta, Srijan |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_04156 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Two-Sample Testing for Multivariate Cross-Correlation Functions with Applications to Gut-Brain Reward Learning Ray, Bhaskar Bùi, Tùng Howe, William Matthew Sengupta, Srijan Applications 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. |
| title | Two-Sample Testing for Multivariate Cross-Correlation Functions with Applications to Gut-Brain Reward Learning |
| topic | Applications |
| url | https://arxiv.org/abs/2604.04156 |