Bayesian inference of high-dimensional, cluster-structured ordinary differential equation models with applications to brain connectivity studies
| Autor: | Yinge Sun, Brian Caffo, Dana Boatman-Reich, Tingting Zhang, Qiannan Yin |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2017 |
| Předmět: |
Statistics and Probability
Bayesian probability Bayesian inference Strong prior Machine learning computer.software_genre 01 natural sciences cluster structure 010104 statistics & probability 03 medical and health sciences symbols.namesake 0302 clinical medicine ODE models 0101 mathematics Mathematics Free energy principle Quantitative Biology::Neurons and Cognition business.industry directional brain networks network edge selection Ode Markov chain Monte Carlo Biological network inference Variable-order Bayesian network Modeling and Simulation symbols Artificial intelligence Statistics Probability and Uncertainty business Algorithm computer 030217 neurology & neurosurgery |
| Zdroj: | Ann. Appl. Stat. 11, no. 2 (2017), 868-897 |
| Popis: | We build a new ordinary differential equation (ODE) model for the directional interaction, also called effective connectivity, among brain regions whose activities are measured by intracranial electrocorticography (ECoG) data. In contrast to existing ODE models that focus on effective connectivity among only a few large anatomic brain regions and that rely on strong prior belief of the existence and strength of the connectivity, the proposed high-dimensional ODE model, motivated by statistical considerations, can be used to explore connectivity among multiple small brain regions. The new model, called the modular and indicator-based dynamic directional model (MIDDM), features a cluster structure, which consists of modules of densely connected brain regions, and uses indicators to differentiate significant and void directional interactions among brain regions. We develop a unified Bayesian framework to quantify uncertainty in the assumed ODE model, identify clusters, select strongly connected brain regions, and make statistical comparison between brain networks across different experimental trials. The prior distributions in the Bayesian model for MIDDM parameters are carefully designed such that the ensuing joint posterior distributions for ODE state functions and the MIDDM parameters have well-defined and easy-to-simulate posterior conditional distributions. To further speed up the posterior simulation, we employ parallel computing schemes in Markov chain Monte Carlo steps. We show that the proposed Bayesian approach outperforms an existing optimization-based ODE estimation method. We apply the proposed method to an auditory electrocorticography dataset and evaluate brain auditory network changes across trials and different auditory stimuli. |
| Databáze: | OpenAIRE |
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