Title: Bayesian variable selection for non-Gaussian responses: A marginally calibrated copula approach
Authors: Nadja Klein - Humboldt University Berlin (Germany) [presenting]
Michael Smith - University of Melbourne (Australia)
Abstract: A new highly flexible and tractable Bayesian approach is proposed to undertake variable selection in non-Gaussian regression models. It uses a copula decomposition for the vector of observations on the dependent variable. This allows the marginal distribution of the dependent variable to be calibrated accurately using a nonparametric or other estimator. The family of copulas employed are 'implicit copulas' that are constructed from existing hierarchical Bayesian models used for variable selection, and we establish some of their properties. Even though the copulas are high-dimensional, they can be estimated efficiently and quickly using Monte Carlo methods. A simulation study shows that when the responses are non-Gaussian, the approach selects variables more accurately than contemporary benchmarks. A marketing example illustrates that accounting for even mild deviations from normality can lead to a substantial improvement. To illustrate the full potential of the approach, we extend it to spatial variable selection for fMRI data. It allows for voxel-specific marginal calibration of the magnetic resonance signal at over 6000 voxels, leading to a considerable increase in the quality of the activation maps.