Using prior-data conflict to tune Bayesian regularized regression models

In high-dimensional regression models, variable selection becomes challenging from a computational and theoretical perspective. Bayesian regularized regression via shrinkage priors like the Laplace or spike-and-slab prior are effective methods for variable selection in p > n scenarios provided the shrinkage priors are configured adequately. We propose configuring shrinkage priors using checks for prior-data conflict: tests that assess whether there is disagreement in parameter information provided by the prior and data. We apply our proposed method to the Bayesian LASSO and spike-and-slab shrinkage priors and assess variable selection performance of our prior configurations against competing models through a linear and logistic high-dimensional simulation study. Additionally, we apply our method to proteomic data collected from patients admitted to the Albany Medical Center in Albany NY in April of 2020 with COVID-like respiratory issues. Simulation results suggest our proposed configurations may outperform competing models when the true regression effects are small.

Name thesis:degree_name

Master of Science (MSc)

Discipline thesis:degree_discipline

Mathematics & Statistics

Grantor dc:publisher.institution

Arts

Year dc:date.issued

2023

Author dc:creator

• Biziaev, Timofei

Advisors dc:contributor.advisor

• Chekouo Tekougang, Thierry
• Kopciuk, Karen A.

Committee members dc:contributor.committeemember

• Deardon, Rob
• Evans, Michael

• Biostatistics
• Bayesian statistics

Statement dc:rights

• University of Calgary graduate students retain copyright ownership and moral rights for their thesis. You may use this material in any way that is permitted by the Copyright Act or through licensing that has been assigned to the document. For uses that are not allowable under copyright legislation or licensing, you are required to seek permission.

Language dc:language.iso

en

DOI

https://doi.org/10.11575/PRISM/42115

OAI identifier oai:identifier

oai:ucalgary.scholaris.ca:1880/117273