A Generalized Bayesian Approach to Distribution-on-Distribution Regression

Tin Lok James Ng

Keywords: Distribution-on-distribution regression, generalized Bayesian, posterior contraction

TL;DR: We propose a generalized Bayesian approach to the problem of distribution-on-distribution regression.

Abstract: In recent years, there has been growing interest in distribution-on-distribution regression, a regression problem where both covariates and responses are represented as probability distributions. Despite various methodologies proposed to address this challenge, a notable absence has been a Bayesian approach, which offers benefits by allowing for the integration of prior knowledge and providing a formal means of quantifying uncertainty. However, a major challenge in employing a Bayesian approach lies in the complexity of fully specifying the data generating process. To overcome this obstacle, we adopt a generalized Bayesian approach and investigate the contraction rates of the resulting generalized (Gibbs) posterior distributions. We propose an MCMC algorithm to sample from the generalized posterior distribution and conduct simulation studies to validate the theoretical findings. Finally, we apply the model to a data application involving mortality data.

List Of Authors: Ng, Tin Lok James

Submission Number: 411