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Abstract:
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Imaging data is increasingly relevant in science, and many applications seek to know which locations are associated with a disease or stimulus. When images are predictors (independent variables) classical linear models break down due to collinearity and/or when the number of image locations nears or exceeds the number of observations. Multiple testing issues also arise and controlling false positive rates while detecting true signal is difficult. Bayesian linear models can address these issues, e.g. in genetic research. We use simulations to evaluate the performance of two prior distribution formulations for Bayesian Generalized Linear Models when scalar outcomes are modeled with image locations as independent variables. One approach uses adaptive shrinkage priors to mostly preserve and significantly shrink estimates for “important” and “unimportant” parameters, respectively, and the other is an adaptation of the Spike-and-Slab LASSO approach, which combines spike-and-slab priors with the shrinkage properties of the LASSO. Both exhibit false positive control and power issues, thus necessitating further research to improve model performance in the presence of spatial correlation.
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