# Bayes-raking: Bayesian Finite Population Inference with Known Margins

## TL;DR

This paper introduces a Bayesian approach to raking in survey inference, incorporating marginal constraints as priors, which improves validity and efficiency, especially with sparse data or dependent factors.

## Contribution

It develops a novel Bayesian framework for raking that integrates constraints as priors, enabling uncertainty propagation and improved inference over traditional methods.

## Key findings

- Bayes-raking performs comparably to traditional raking with large samples.
- It outperforms in validity and efficiency with sparse tables or dependent factors.
- Application to wellbeing data shows improved inferential reliability.

## Abstract

Raking is widely used in categorical data modeling and survey practice but faced with methodological and computational challenges. We develop a Bayesian paradigm for raking by incorporating the marginal constraints as a prior distribution via two main strategies: 1) constructing the solution subspaces via basis functions or projection matrix and 2) modeling soft constraints. The proposed Bayes-raking estimation integrates the models for the margins, the sample selection and response mechanism, and the outcome, with the capability to propagate all sources of uncertainty. Computation is done via Stan, and codes are ready for public use. Simulation studies show that Bayes-raking can perform as well as raking with large samples and outperform in terms of validity and efficiency gains, especially with a sparse contingency table or dependent raking factors. We apply the new method to the Longitudinal Study of Wellbeing study and demonstrate that model-based approaches significantly improve inferential reliability and substantive findings as a unified survey inference framework.