Bayesian variable selection in circular regression models using lasso

Çamlı, Onur
Applications of circular regression models are ubiquitous in many disciplines, particularly in meteorology, biology and geology. In these models, variable selection problem continues to be a remarkable open question. In this thesis, inspired by the Bayesian lasso used in Euclidean space, we consider new shrinkage-based approaches for variable selection in circular regression models. Firstly, we adapt Bayesian lasso for linear-circular regression models and show that it is not able to produce robust inference as the coefficient estimates are sensitive to the choice of hyper-prior setting for the tuning parameter. To eradicate the problem, we propose a robustified Bayesian lasso that is based on an empirical Bayes (EB) type methodology to construct a hyperprior for the tuning parameter. This construction is computationally feasible and can be used effectively in both Euclidean and circular regression settings. Simulation studies show that robustified Bayesian lasso leads to a more robust inference. Then, we compare the performance of our proposed method and the existing prior distributions in the literature using two different real data sets. Overall, the method offers an efficient Bayesian lasso for variable selection in linear-circular regression. Secondly, we adapted Bayesian lasso and Bayesian adaptive lasso methods that can allow for individual shrinking coefficients for each coefficient in circular-(circular, linear) regression models. We also develeoped some alternatives of Bayesian adaptive lasso based on Dirichlet Process prior. In this context, we provide a comprehensive simulation study to show the performances and behavior of the adapted and proposed methodologies in terms of parameter estimation and variable selection. The results indicate that the different methods being compared have similar performance based on evaluation metrics for both parameter estimation and variable selection in circular- (circular, linear) regression models.
Citation Formats
O. Çamlı, “Bayesian variable selection in circular regression models using lasso,” Ph.D. - Doctoral Program, Middle East Technical University, 2023.