Calibrated Bayes, for Statistics in General, and Missing Data in Particular

TL;DR

This paper advocates for the Calibrated Bayesian approach, which combines Bayesian inference with frequentist model checking, especially for handling missing data through advanced Bayesian methods and imputation techniques.

Contribution

It outlines the CB framework, reviews Bayesian methods for missing data, and introduces practical approaches like Sequential Regression Multivariate Imputation and Penalized Spline of Propensity Models.

Findings

Bayesian methods effectively handle missing data in normal models.

Sequential Regression Multivariate Imputation improves imputation accuracy.

Penalized Spline of Propensity Models relax distributional assumptions.

Abstract

It is argued that the Calibrated Bayesian (CB) approach to statistical inference capitalizes on the strength of Bayesian and frequentist approaches to statistical inference. In the CB approach, inferences under a particular model are Bayesian, but frequentist methods are useful for model development and model checking. In this article the CB approach is outlined. Bayesian methods for missing data are then reviewed from a CB perspective. The basic theory of the Bayesian approach, and the closely related technique of multiple imputation, is described. Then applications of the Bayesian approach to normal models are described, both for monotone and nonmonotone missing data patterns. Sequential Regression Multivariate Imputation and Penalized Spline of Propensity Models are presented as two useful approaches for relaxing distributional assumptions.