Modern regression analyses are often undermined by covariate measurement error, misspecification of the regression model, and misspecification of the measurement error distribution. We present, to the best of our knowledge, the first Bayesian nonparametric learning framework targeting total robustness to all three challenges in general nonlinear regression. Our framework places a joint Dirichlet process prior on the latent covariate--response distribution and updates it with posterior pseudo-samples of the latent covariates, so that inference is calibrated to the joint law. This yields estimators defined by minimizing the discrepancy between posterior realizations of the joint Dirichlet process and the model-implied joint distribution. We establish generalization bounds and provide a first proof of convergence and consistency of the resulting estimators under non-degenerate measurement error. A gradient-based implementation enables efficient computation; simulations and two real-data studies show improved stability to misspecification under increasing measurement error relative to recent Bayesian and frequentist alternatives.

翻译：现代回归分析常受到协变量测量误差、回归模型误设以及测量误差分布误设的影响。我们首次提出了一个贝叶斯非参数学习框架，旨在针对一般非线性回归中的这三类挑战实现总稳健性。该框架在潜在协变量-响应联合分布上施加狄利克雷过程先验，并通过潜在协变量的后验伪样本对其进行更新，从而使推断与联合分布校准。由此得到的估计量通过最小化联合狄利克雷过程的后验实现与模型隐含的联合分布之间的差异来定义。我们建立了泛化界，并首次证明了在非退化测量误差下所得估计量的收敛性和一致性。基于梯度的实现方法支持高效计算；模拟实验及两项实际数据研究表明，与近年来的贝叶斯和频率学派替代方法相比，该方法在测量误差增大时对误设具有更优的稳定性。