Bayesian variable selection with spike-and-slab priors
Anjali Agarwal · OhioLink ETD Center (Ohio Library and Information Network) · 2016
A major focus of intensive methodological research in recent times has been on knowledge extraction from high-dimensional datasets made available by advances in research technologies.Coupled with the growing popularity of Bayesian methods in statistical analysis, a range of new techniques have evolved that allow innovative model-building and inference in high-dimensional settings -an important one among these being Bayesian variable selection (BVS).The broad goal of this thesis is to explore different BVS methods and demonstrate their application in high-dimensional psychological data analysis.In particular, the focus will be on a class of sparsity-enforcing priors called 'spike-and-slab' priors which are mixture priors on regression coefficients with density functions that are peaked at zero (the 'spike') and also have large probability mass for a wide range of non-zero values (the 'slab').It is demonstrated that BVS with spike-and-slab priors achieved a reasonable degree of dimensionality-reduction when applied to a psychiatric dataset in a logistic regression setup.BVS performance was also compared to that of LASSO (least absolute shrinkage and selection operator), a popular machine-learning technique, as reported in Ahn et al.(2016).The findings indicate that BVS with a spike-and-slab prior provides a competitive alternative to machine-learning methods, with the additional advantages of ease of interpretation and potential to handle more complex models.In conclusion, this thesis serves to add a new cutting-edge technique to the lab's tool-shed and helps introduce Bayesian variable-selection to researchers in Cognitive Psychology where it still remains relatively unexplored as a dimensionality-reduction tool.