Dataset Information

High-Dimensional Posterior Consistency in Bayesian Vector Autoregressive Models.

ABSTRACT: Vector autoregressive (VAR) models aim to capture linear temporal interdependencies amongst multiple time series. They have been widely used in macroeconomics and financial econometrics and more recently have found novel applications in functional genomics and neuroscience. These applications have also accentuated the need to investigate the behavior of the VAR model in a high-dimensional regime, which provides novel insights into the role of temporal dependence for regularized estimates of the model's parameters. However, hardly anything is known regarding properties of the posterior distribution for Bayesian VAR models in such regimes. In this work, we consider a VAR model with two prior choices for the autoregressive coefficient matrix: a non-hierarchical matrix-normal prior and a hierarchical prior, which corresponds to an arbitrary scale mixture of normals. We establish posterior consistency for both these priors under standard regularity assumptions, when the dimension p of the VAR model grows with the sample size n (but still remains smaller than n). A special case corresponds to a shrinkage prior that introduces (group) sparsity in the columns of the model coefficient matrices. The performance of the model estimates are illustrated on synthetic and real macroeconomic data sets.

SUBMITTER: Ghosh S

PROVIDER: S-EPMC6716151 | biostudies-literature | 2019

REPOSITORIES: biostudies-literature

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Publications

High-Dimensional Posterior Consistency in Bayesian Vector Autoregressive Models.

Ghosh Satyajit S Khare Kshitij K Michailidis George G

Journal of the American Statistical Association 20180807 526

Vector autoregressive (VAR) models aim to capture linear temporal interdependencies amongst multiple time series. They have been widely used in macroeconomics and financial econometrics and more recently have found novel applications in functional genomics and neuroscience. These applications have also accentuated the need to investigate the behavior of the VAR model in a high-dimensional regime, which provides novel insights into the role of temporal dependence for regularized estimates of the ...[more]

PMID: 31474783

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Project description:Fundamental to elucidating the functional organization of the brain is the assessment of causal interactions between different brain regions. Multivariate autoregressive (MVAR) modeling techniques applied to multisite electrophysiological recordings are a promising avenue for identifying such causal links. They estimate the degree to which past activity in one or more brain regions is predictive of another region's present activity, while simultaneously accounting for the mediating effects of other regions. Including as many mediating variables as possible in the model has the benefit of drastically reducing the odds of detecting spurious causal connectivity. However, effective bounds on the number of MVAR model coefficients that can be estimated reliably from limited data make exploiting the potential of MVAR models challenging for even modest numbers of recording sites. Here, we utilize well-established dimensionality-reduction techniques to fit MVAR models to human intracranial data from ∼100 - 200 recording sites spanning dozens of anatomically and functionally distinct cortical regions. First, we show that high-dimensional MVAR models can be successfully estimated from long segments of data and yield plausible connectivity profiles. Next, we use these models to generate synthetic data with known ground-truth connectivity to explore the utility of applying principal component analysis and group least absolute shrinkage and selection operator (gLASSO) to reduce the number of parameters (connections) during model fitting to shorter data segments. We show that gLASSO is highly effective for recovering ground-truth connectivity in the limited data regime, capturing important features of connectivity for high-dimensional models with as little as 10 seconds of data. The methods presented here have broad applicability to the analysis of high-dimensional time series data in neuroscience, facilitating the elucidation of the neural basis of sensation, cognition, and arousal.

Dataset Information

High-Dimensional Posterior Consistency in Bayesian Vector Autoregressive Models.

Publications

High-Dimensional Posterior Consistency in Bayesian Vector Autoregressive Models.

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