Monte Carlo inference for semiparametric Bayesian regression.

Area of Science:

• Statistics
• Bayesian Inference
• Semiparametric Modeling

Background:

• Parametric regression models require data transformations for broad applicability.
• Existing Bayesian methods for joint inference of transformations and parameters are computationally inefficient and theoretically cumbersome.
• This limits the practical usability of Bayesian approaches in data analysis.

Purpose of the Study:

• To introduce a simple, general, and efficient strategy for joint posterior inference of unknown data transformations and regression model parameters.
• To overcome the limitations of existing Bayesian methods for transformation inference.
• To provide tools applicable across diverse data domains.

Main Methods:

• Directly targeting the posterior distribution of the transformation by linking it with marginal distributions of variables.
• Employing a Bayesian nonparametric model through the Bayesian bootstrap.
• Developing efficient Monte Carlo inference, distinct from Markov chain Monte Carlo.

Main Results:

• The proposed approach achieves joint posterior consistency under general conditions, including model misspecification.
• Efficient Monte Carlo inference is delivered for transformations and model parameters in key special cases.
• The strategy is effective across real-valued, positive, and compactly-supported data.

Conclusions:

• The developed strategy offers a significant advancement for semiparametric Bayesian analysis.
• It enhances the usability and efficiency of Bayesian regression models with unknown transformations.
• The R package SeBR facilitates the practical application of these methods.