论文标题
贝叶斯反回归和反参考分布的后验一致性
Posterior Consistency of Bayesian Inverse Regression and Inverse Reference Distributions
论文作者
论文摘要
我们考虑在反回归问题中推断贝叶斯的推断，在这些问题中，目的是从观察到的反应和协变量中推断出未观察到的协变量。我们在贝叶斯逆回归问题中的这种未观察到的协变量在适当的先验中的贝叶斯反回归问题中建立了后验一致性。我们将其与反向参考分布（Bhattacharya（2013））的后验一致性相关联，以评估模型充分性。我们用贝叶斯反回归的各种示例以及足够的模拟实验来说明我们的理论和方法。
We consider Bayesian inference in inverse regression problems where the objective is to infer about unobserved covariates from observed responses and covariates. We establish posterior consistency of such unobserved covariates in Bayesian inverse regression problemsunder appropriate priors in a leave-one-out cross-validation setup. We relate this to posterior consistency of inverse reference distributions (Bhattacharya (2013)) for assessing model adequacy. We illustrate our theory and methods with various examples of Bayesian inverse regression, along with adequate simulation experiments.
