Graphical network and topology estimation for autoregressive models using Gibbs sampling

In this paper, we propose novel strategies based on Gibbs sampling for the estimation of the coefficients and topology of a graphical network represented by a first-order vector autoregressive model. As the topology and the coefficients are closely related, obtaining their Markov chains together is a nontrivial task. When incorporating both in a Gibbs-based sampler, the topology samples at each iteration are decisive factors in how information for the corresponding coefficient samples is propagated. We propose new Gibbs-based samplers that differ in the sampling strategies and scanning order used for their operation. We ran a series of experiments on simulated data to analyze and compare the samplers’ performances with dimension of data, data size, and choice of prior. The best performing sampler was also applied to real data related to a financial network. Converged Markov chains of coefficient and topology elements of the network attest to the method's validity, and plots illustrating posterior distributions of the predicted data against the observed data indicate promising inference for real data applications.