3rd Floor Classroom/3-Flatiron Institute (162 5th Avenue)
3rd Floor Classroom/3-Flatiron Institute
162 5th Avenue
40
Description
Speaker: Sarah Heaps
Bio: Associate Professor in Statistics at Durham University in Durham, England, and a Fellow of the Alan Turing Institute. Sarah's research lies in the field of Bayesian inference, where special interests are multivariate time series analysis and the development of structured prior distributions for multivariate parameters. Her interdisciplinary research spans applications in phylogenetics, metagenomics, earth sciences and engineering.
Title: Bayesian inference on the order of stationary vector autoregressions
Abstract: Vector autoregressions (VARs) have an associated order p; given observations at the preceding p time-points, the variable at time t is conditionally-independent of all earlier history. Learning the order of the model is therefore vital for its characterization and use in forecasting. It is often useful to assume a VAR is stationary; a VAR is stable if and only if the roots of its characteristic equation lie outside the unit circle, constraining the autoregressive coefficient matrices to the stationary region. Unfortunately, the geometry of the stationary region is complicated which impedes specification of a prior. In this work, the autoregressive coefficients are mapped to a set of transformed partial autocorrelation matrices which are unconstrained and amenable to Bayesian inference. The multiplicative gamma process is used to build a prior which encourages increasing shrinkage of the partial autocorrelations with increasing lag. Identifying the lag beyond which the partial autocorrelations become equal to zero then determines p. Posterior inference utilizes Hamiltonian Monte Carlo via Stan. Based on classic time-series theory, a principled choice of truncation criterion identifies whether a partial autocorrelation matrix is effectively zero. The work is applied to neural activity data to investigate ultradian rhythms in the brain.
