# An Approximate Bayesian Approach to Model-assisted Survey Estimation with Many Auxiliary Variables

## TL;DR

This paper introduces a Bayesian regularized regression method for model-assisted survey estimation with many auxiliary variables, providing efficient estimates and credible intervals, demonstrated through simulation studies.

## Contribution

It proposes a novel Bayesian approach using shrinkage priors for variable selection in survey estimation with numerous auxiliary variables.

## Key findings

- The method yields efficient point estimates.
- It provides credible intervals with good coverage.
- Simulation results compare favorably with frequentist methods.

## Abstract

Model-assisted estimation with complex survey data is an important practical problem in survey sampling. When there are many auxiliary variables, selecting significant variables associated with the study variable would be necessary to achieve efficient estimation of population parameters of interest. In this paper, we formulate a regularized regression estimator in the framework of Bayesian inference using the penalty function as the shrinkage prior for model selection. The proposed Bayesian approach enables us to get not only efficient point estimates but also reasonable credible intervals. Results from two limited simulation studies are presented to facilitate comparison with existing frequentist methods.