ISBA World Meeting 2021. Short Course 2: Advanced Topics in Variable Selection and Model Averaging

Описание: Speakers
Joseph Antonelli, University of Florida, Department of Statistics,
Antonio Linero, University of Texas at Austin

In this course we will cover a wide range of topics related to variable selection and model averaging within the Bayesian paradigm. We will begin with the standard linear regression model where we will discuss issues relating to prior choice, implementation, and theory. Practical issues such as the sensitivity to the prior distribution will be illustrated through examples. We will then move to more complex regression models, showing how the same ideas can be applied with little additional effort. We will first move to additive models that drop the linearity assumption for each covariate. We will illustrate these ideas using flexible parametric specifications, and then we will move towards fully nonparametric Gaussian process priors as a means to flexible regression modeling, and how these can also easily accommodate variable selection through spike-and-slab prior distributions. Next, the additivity assumption will be dropped and we will move to Bayesian models that allow for interactions among each covariate within the regression model. In particular, we will focus on tree-based models and how they can be coupled with sparsity-inducing priors to simultaneously allow for highly flexible modeling and variable selection. All of these ideas will be presented with the goal that attendees will be able to apply these methods after taking the course. For this reason, all derivations of conditional distributions for Gibbs samplers will be provided along with R codes and data sets that are used throughout the course.