Title: Structured prior distributions for the covariance matrix in latent factor models
Authors: Sarah Elizabeth Heaps - Durham University (United Kingdom) [presenting]
Abstract: Factor models are widely used for dimension reduction in the analysis of multivariate data. This is achieved through a (sparse) factorisation of a $p\times p$ covariance matrix; a latent factor representation allows this to be interpreted as the sum of a diagonal matrix of idiosyncratic variances and a shared variation matrix equal to the product of a $p \times k$ factor loadings matrix ($k << p$) and its transpose. Historically, little attention has been paid to incorporating prior information in Bayesian analyses using factor models where, at best, the prior for the factor loadings matrix is invariant with respect to the order of the variables. A class of structured priors is developed that can encode ideas of dependence structure about the shared variation matrix. The construction allows data-informed shrinkage towards sensible parametric structures within a framework that facilitates inference on the number of factors. Using an unconstrained reparameterisation of stationary vector autoregressions, the methodology is also extended to stationary dynamic factor models. For computational inference, parameter-expanded Markov chain Monte Carlo samplers are proposed, including an efficient adaptive Gibbs sampler. Finally, substantive applications showcase the scope of the methodology and its inferential benefits.