Efficient Bayesian Variable Selection under Predictor Dependence Regimes

Thomas M. Menino Convention & Exhibition Center 

We propose a computationally scalable Bayesian variable selection
framework that incorporates dependence structures among predictors
while remaining robust to hyperparameter specification. By introducing
a latent continuous variable and a Gaussian Markov random field prior
within a discrete spike-and-slab framework, our approach circumvents
the phase transition problems that typically plague binary Markov
random field priors. To ensure scalability, we develop an algorithmic
design that exploits the model's algebraic structure. This enables
fast, numerically stable updates of posterior quantities and
eliminates the need for repeated matrix inversions without
compromising inferential accuracy. We demonstrate the method's
superior performance and computational efficiency through simulation
studies and illustrate its practical utility using high-dimensional
genomic data.

Bayesian variable selection

Spike-and-slab priors

Bayesian inference

Scalable algorithms

Predictor dependence

Large-scale genomic data 

Section on Bayesian Statistical Science