CMStatistics 2022: Start Registration
View Submission - CMStatistics
Title: Bayesian cumulative shrinkage for infinite factorizations Authors:  Sirio Legramanti - University of Bergamo (Italy) [presenting]
Daniele Durante - Bocconi University (Italy)
David Dunson - Duke University (United States)
Abstract: The dimension of the parameter space is typically unknown in a variety of models that rely on factorizations. For example, in factor analysis, the number of latent factors is not known and has to be inferred from the data. Although classical shrinkage priors are useful in such contexts, increasing shrinkage priors can provide a more effective approach that progressively penalizes expansions with growing complexity. We propose a novel increasing shrinkage prior, called the cumulative shrinkage process, for the parameters that control the dimension in overcomplete formulations. Our construction has broad applicability and is based on an interpretable sequence of spike-and-slab distributions which assign increasing mass to the spike as the model complexity grows. Using factor analysis as an illustrative example, we show that this formulation has theoretical and practical advantages relative to current competitors, including an improved ability to recover the model dimension. An adaptive Markov chain Monte Carlo algorithm is proposed, and the performance gains are outlined in simulations and in an application to personality data.