A Bayesian Approach to Inferring Conditional Independencies for Stationary Time Series

• Activity Number: 263
• Type: Contributed
• Date/Time: Monday, August 10, 2015 : 2:00 PM to 3:50 PM
• Sponsor: Section on Bayesian Statistical Science
• Author(s): Alex Tank* and Nicholas Foti and Emily Fox
• Companies: and University of Washington and University of Washington
• Keywords: Time Series ; Bayesian ; Graphical Models

Abstract

While much work has explored conditional independence graphs (CIG) for independent data, less attention has been paid to dependent data like time series. The goal in this setting is to determine conditional independence relations between entire time series. For stationary series, the CIG is given by zeros in the inverse spectral density matrix for all frequencies. We take a Bayesian approach and use the Whittle approximation to recast the likelihood into a product of independent complex normal distributions. Each term in the product gives the likelihood of observing the Fourier coefficients at a frequency given the spectral density. We introduce the hyper inverse complex Wishart as a prior over complex matrices with a zero pattern specified by a graph. Given a graph, this prior is placed independently on each spectral matrix in the Whittle approximation. By marginalizing out the spectral matrices, we obtain the marginal likelihood given a CIG. Combining this term with a prior over graphs allows for inference of the CIG itself, which we base on a MCMC scheme. The decomposition of the marginal likelihood across frequencies invites parallelization, scaling the method to long series.