Inference from Non-Random Samples Using Bayesian Machine Learning

TL;DR

This paper introduces a Bayesian machine learning approach for inference from non-random samples, leveraging auxiliary variables and propensity scores to improve population estimates with valid uncertainty quantification.

Contribution

It develops a regularized prediction method using Bayesian additive regression trees that accounts for non-random sampling and incorporates propensity scores for better inference.

Findings

Valid population mean inference achieved in simulations

Coverage rates close to nominal levels

Effective application demonstrated in survey and epidemiology data

Abstract

We consider inference from non-random samples in data-rich settings where high-dimensional auxiliary information is available both in the sample and the target population, with survey inference being a special case. We propose a regularized prediction approach that predicts the outcomes in the population using a large number of auxiliary variables such that the ignorability assumption is reasonable while the Bayesian framework is straightforward for quantification of uncertainty. Besides the auxiliary variables, inspired by Little & An (2004), we also extend the approach by estimating the propensity score for a unit to be included in the sample and also including it as a predictor in the machine learning models. We show through simulation studies that the regularized predictions using soft Bayesian additive regression trees yield valid inference for the population means and coverage rates close to the nominal levels. We demonstrate the application of the proposed methods using two different real data applications, one in a survey and one in an epidemiology study.