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RESCHEDULED: Math. Kolloquium: Bayesian Variable Selection for Non-Gaussian Responses | Prof. Katja Klein

Veranstalter: Prof. Jens Rademacher / Prof. Christine Knipping
Beginn: 09. Juni 2020, 16:00 Uhr
Ende: 09. Juni 2020, 17:30 Uhr
Kategorie: Fachbereich 03 - Veranstaltungen

We propose a new highly  flexible and tractable Bayesian approach 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. To illustrate the full potential of our 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 6,000 voxels, leading to an increase in the quality of the activation maps.