Advances in research technologies make high-dimensional data available, and the most interesting research has been conducted on variable selection. The Bayesian variable selection is gaining interest in different fields because of its vast literature. In this paper our main objective is to investigate Bayesian variable selection (BVS) in the context of a random effect model using various prior for variance components in the spike-slab prior approach.
The spike-slab prior is viewed as a mixture distribution, where some regression coefficients concentrate around zero (spike), and the remaining coefficients have a probability of not being zero values (slab). Generally, for building a model, the normal distribution is considered a prior for regression coefficients in the spike-slab components. When the variance is unknown in normal, it could be estimated by extending the model into a hierarchical model. In a hierarchical model, different prior distributions have been proposed for the variance components. Generally, the prior distributions chosen for the variance component are uniform, inverse gamma, and half-Cauchy distribution. Both simulation and real data will be studied to investigate and evaluate how good the chosen distribution for variance components is in the random effect model for the spike-slab approach.
The application of the BVS with spike-slab prior to microarray data from ADNI (Alzheimer’s Disease Neuroimaging Initiative), in a logistic regression setting (Alzheimer’s Disease vs. Control) demonstrated a notable degree of dimensionality reduction. These selected genes maintain lower misclassification error percentages with higher area under the receiver operating characteristic curve( AUC-ROC) values in different machine-learning algorithms. This discovery opens up new avenues for in-depth exploration and investigation, potentially leading to the identification of biomarkers for Alzheimer’s Disease(AD).
Md Maidul Husain & Anwar Hossain(2024). Bayesian Variable Selection with Spike-Slab prior in Random effect Model, Journal of Applied Statistics & Machine Learning, 3(1-2), pp. 41-61.