Abstract: Data transformations are essential for broad applicability of parametric regression
models. However, for Bayesian analysis, joint inference of the transformation and
model parameters typically involves restrictive parametric transformations or
nonparametric representations that are computationally inefficient and
cumbersome for implementation and theoretical analysis, which limits their
usability in practice. We introduce a simple, general, and efficient strategy for joint
posterior inference of an unknown transformation and all regression model
parameters. The proposed approach directly targets the posterior distribution of
the transformation by linking it with the marginal distributions of the independent
and dependent variables, and then deploys a Bayesian nonparametric model via the
Bayesian bootstrap. Crucially, this approach delivers (1) joint posterior consistency
under general conditions, including multiple model misspecifications, and (2)
efficient Monte Carlo (not Markov chain Monte Carlo) inference for the
transformation and all parameters for important special cases. These tools apply
across a variety of data domains, including real-valued, positive, and compactly-
supported data. Simulation studies and an empirical application demonstrate the
effectiveness and efficiency of this strategy for semiparametric Bayesian analysis
with linear models, quantile regression, and Gaussian processes. The R package
SeBR is available on CRAN.
Paper: https://doi.org/10.1080/01621459.2024.2395586
Software documentation: https://drkowal.github.io/SeBR/

Bio: Dan Kowal is Associate Professor in the Department of Statistics and Data Science at Cornell University. His research interests include Bayesian models and algorithms for dependent data, synthesis and imputation of mixed data, and issues related to statistical interpretability and equity. Dr. Kowal’s research has been recognized with a Young Investigator Award from the Army Research Office, the inaugural Blackwell-Rosenbluth Award, and multiple paper and presentation awards.