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. This paper introduces 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.

翻译：数据变换对于参数回归模型的广泛适用性至关重要。然而，在贝叶斯分析中，变换与模型参数的联合推断通常涉及限制性的参数变换或计算效率低下、实现与理论分析繁琐的非参数表示，这限制了它们在实践中的可用性。本文提出了一种简单、通用且高效的策略，用于对未知变换及所有回归模型参数进行联合后验推断。所提方法通过将变换与自变量及因变量的边际分布相关联，直接以变换的后验分布为目标，并借助贝叶斯自助法部署贝叶斯非参数模型。关键的是，该方法实现了（1）在包括多重模型误设在内的通用条件下的联合后验一致性，以及（2）针对重要特例的变换与所有参数的高效蒙特卡洛（非马尔可夫链蒙特卡洛）推断。这些工具适用于多种数据领域，包括实值数据、正值数据及紧支集数据。仿真研究及实证应用证明了该策略在线性模型、分位数回归和高斯过程等半参数贝叶斯分析中的有效性与高效性。R 软件包 SeBR 已在 CRAN 上发布。