Bayesian Feature Extraction using Gaussian and Diffused-gamma Priors for High Dimensional Spatio-Temporal Data

High-dimensional data with sparse structure and spatio-temporal dependence arise in many scientific domains. We develop a Bayesian feature-extraction framework for spatio-temporal settings that employs Gaussian and Diffused-gamma priors to induce structured sparsity. The modeling framework specifies a general likelihood via Bregman divergence, enabling compatibility with a range of loss functions and measurement models. Posterior computation is carried out via Markov chain Monte Carlo (MCMC), and we introduce a two-stage feature-extraction procedure based on posterior samples to stabilize selection across space and time. We illustrate the method with a multi-subject electroencephalography (EEG) case study examining the relationship between chronic alcohol exposure and activity in different brain regions. We first fit binary classification models at each time point, then use false discovery rate-controlled screening and subsequent clustering in a two-stage feature-extraction pipeline to identify active brain regions. The analysis demonstrates that our proposed priors improve recovery of sparse features and enhance interpretability in the presence of spatio-temporal dependence. The framework is broadly applicable to high-dimensional, structured problems where accurate feature selection and inference are required. The code to implement the model is publicly available via GitHub.

Variance or Standard Deviation? Shell Geometry and Global-Scale Priors in High-Dimensional Shrinkage

We study how the choice of default prior for a common Gaussian scale affects high-dimensional shrinkage risk, highlighting the role played by high-dimensional geometry. Formally, we consider a high-dimensional setting in which the near-zero behavior of the common scale prior has first-order consequences for shrinkage risk, and show that priors that are flat on the variance and those flat on the standard deviation allocate markedly different mass near the zero-scale boundary, leading to distinct shrinkage behavior and informing principled default prior selection. Specifically, under a radial-power benchmark, we establish that the SD-flat benchmark has a one-unit asymptotic risk advantage near the origin, crosses over in the critical regime, and is second-order equivalent to the variance-flat benchmark for strong signals. Proper single global-scale hyperpriors and bounded coordinate-multiplier mixtures inherit these limits through the near-zero exponent of their SD-scale density. For heavier-tailed or sparse priors, that exponent still classifies the common global-scale component, while local-scale tails, model-size priors, or allocation priors can also affect risk.