Abstract:
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Spike-and-slab priors assume predictors arise from a mixture of distributions: those that should (slab) or should not (spike) remain in the model. The spike-and-slab lasso (SSL) is a mixture of double exponentials, extending the single lasso penalty by imposing different penalties on parameter based on their inclusion probabilities. The SSL was extended to Generalized Linear Models (GLM) for application in genetics/genomics, and can handle many highly correlated predictors, but does not incorporate structured correlation into variable selection. When predictors exhibit spatial dependence, parameters that should be included in the model tend to cluster spatially, and thus model performance may benefit from incorporating spatial structure into the model. We propose a new model to incorporate spatial information by assigning conditional autoregressive priors to the logit of prior probabilities of inclusion, which affects the shrinkage of parameter estimates such that spatially adjacent parameters are more likely to have similar shrinkage penalties. We also discuss and illustrate how to estimate the model using an EM algorithm.
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