“Fast algorithms and theory for high-dimensional Bayesian varying coefficient models” (Poster)
January 8, 2020, Bayes Comp 2020, University of Florida, Gainesville, FL
We introduce the nonparametric varying coefficient spike-and-slab lasso (NVC-SSL) for Bayesian estimation and variable selection in high-dimensional varying coefficient models. The NVC-SSL simultaneously estimates the functionals of the significant time-varying covariates while thresholding out insignificant ones. Our model can be implemented using a highly efficient expectation-maximization (EM) algorithm, thus avoiding the computational intensiveness of Markov chain Monte Carlo (MCMC) in high dimensions. Finally, we prove the first theoretical results for Bayesian varying coefficient models when p>>n. Specifically, we derive posterior contraction rates under the NVC-SSL model. Our method is illustrated through simulation studies and data analysis.
“A robust Bayesian Copas selection model for detecting and correcting publication bias”
The validity of conclusions from meta-analysis is potentially threatened by publication bias. Most existing procedures for handling this issue decouple testing for the presence of publication bias from estimation of unknown parameters under publication bias. Most of these procedures also assume normality of the between-study random effects. This assumption may be invalid, especially if there are outliers in the studies included in the meta-analysis. Finally, there exist few procedures to quantify the magnitude of publication bias. In this talk, we simultaneously address all of these issues. First, we introduce the robust Bayesian Copas (RBC) selection model, which unifies inference and estimation and which offers robustness to strong assumptions about the distribution of the random effects. Second, we develop two new measures to quantify the magnitude of publication bias: one based on point estimates which can also be used for non-Bayesian methods, and one based on the posterior distribution. We illustrate our method through simulations and two case studies.
“Fast variable selection and estimation in high-dimensional Bayesian nonparametric additive models without MCMC” (Invited session on Bayesian variable selection at the Fifth EAC-ISBA Conference: A Satellite Meeting of the 2020 ISBA World Meeting in Celebrating James O Berger’s 70th Birthday)
June 26-27, 2020, Dali, Yunnan, China
The linear regression model is widely used but the assumption of linearity is often very restrictive and easily violated in practice. Generalized additive models (GAMs) provide an avenue to remove such a restrictive assumption and model nonlinear regression surfaces. In this talk, we introduce a new Bayesian approach to estimation and variable selection in high-dimensional GAMs using a new prior known as the spike-and-slab group lasso (SSGL). This model can be implemented with a highly efficient block-coordinate ascent algorithm, allowing us to bypass computationally intensive algorithms like MCMC. Uncertainty quantification for our model is also made possible by using de-biasing methods rather than posterior simulation.