A1601
Title: Sparse dynamic Bayesian graphical models
Authors: Luis Gruber - University of Klagenfurt (Austria)
Matteo Iacopini - LUISS Guido Carli (Italy)
Gregor Kastner - University of Klagenfurt (Austria) [presenting]
Abstract: Gaussian graphical models have become a staple in statistical modelling and for estimating partial correlation networks. The baseline approach is extended to a time series framework by introducing temporal dependence for the entries of the precision matrix. In order to conduct statistical inference, a fully Bayesian approach is adopted, relying on global-local shrinkage priors to deal with high-dimensional data and mitigate (temporal) overfitting. The framework has several special cases of interest, including a variant of the standard Bayesian graphical lasso. Closed-form recursions for the filtering and smoothing distributions are obtained. These results are exploited to design a simple yet efficient blocked Gibbs sampler for posterior inference. An interweaving strategy is applied to enhance the mixing of the sampler. As a by-product, the proposed method allows for estimating a time series of (sequentially dependent) networks from partial correlations among the variables in the system. Using synthetic and real data, the performance of the model is investigated in comparison to standard Bayesian and frequentist benchmarks in terms of both covariance matrix estimation and graphical structure learning.
