A0952
Title: Fast Bayesian model selection algorithms for linear regression models
Authors: Mauro Bernardi - University of Padova (Italy) [presenting]
Manuela Cattelan - University of Padova (Italy)
Claudio Busatto - University of Florence (Italy)
Abstract: The challenge of model selection in high-dimensional linear regression has traditionally been tackled by assuming hierarchical mixtures as prior distributions. To exclude irrelevant covariates, a spike component with Dirac probability mass at zero is introduced, leading to Bayesian selection procedures based on the marginal posterior distribution of various model configurations. Exploring the space of competing models involves computationally intensive simulation techniques. The issue of efficiently updating the variance-covariance matrix of the posterior distribution and the marginal posterior density following a change in the design matrix is addressed. Using thin QR factorization, novel algorithms are proposed to update the posterior variance-covariance matrix without storing and updating the Q matrix, resulting in significant computational savings. Furthermore, the focus is on evaluating the marginal posterior, a critical bottleneck in Bayesian model selection. The approach shows that computing the marginal posterior depends on the inverse of the R matrix. Thus, a methodology is developed to update both this inverse and the associated marginal posterior after modifying the design matrix. These methods eliminate the need for computationally intensive inversions of large matrices when evaluating the marginal posterior.
