Posterior Consistency of Bayesian Inverse Regression and Inverse Reference Distributions

2020/05/01 by Debashis Chatterjee, Chatterjee, Debashis, Sourabh Bhattacharya +1 · 1 citation
Computer Science · Mathematics · #Bayesian Methods and Mixture Models #FOS: Mathematics #Gaussian Processes and Bayesian Inference #Statistical Methods and Inference #Statistics Theory (math.ST)

paper · pdf · doi:10.48550/arxiv.2005.00236

openalex publication_date 2020/05/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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.

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