# Hierarchical Gaussian Processes for Survey Weighting: Local Equivalent Weights in Structured Populations

arXiv: https://arxiv.org/abs/2610.20321 · HTML: https://mlsanity.com/paper/2610.20321/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 6 of its 26 references that are in the map.
- First posted on arXiv 14 Oct 2026.

## Builds on (most cited first, 6 of 6)

- [Dealing with Integer-valued Variables in Bayesian Optimization with Gaussian Processes](https://mlsanity.com/paper/1706.03673/) (2017)
- [Group kernels for Gaussian process metamodels with categorical inputs](https://mlsanity.com/paper/1802.02368/) (2018)
- [Bayesian Nonparametric Weighted Sampling Inference](https://mlsanity.com/paper/1309.1799/) (2013)
- [Bayesian hierarchical weighting adjustment and survey inference](https://mlsanity.com/paper/1707.08220/) (2017)
- [Bayesian Inference under Cluster Sampling with Probability Proportional to Size](https://mlsanity.com/paper/1710.00959/) (2017)
- [Logistic Regression Equivalent Weights for Survey Inference: Construction and Asymptotic Properties](https://mlsanity.com/paper/2608.22732/) (2026)

## Abstract (arXiv)

Regression-based survey weighting connects model-based population estimation with design-based inference through equivalent weights. For nonlinear models, equivalent weights can be defined locally through the sensitivity of a poststratified population estimator. However, conventional regression models may inadequately capture nonlinear relationships and complex interactions across sparse poststratification cells. We develop a survey-weighting framework based on hierarchical Gaussian process (HGP) regression, combining structured group-level effects with kernel-based smoothing to share information across related cells. We derive Gaussian posterior prediction formulas that exploit the structured covariance representation to reduce computational costs. We also establish a uniform convergence result for the posterior predictive mean under stated regularity conditions and construct local equivalent weights by matching the first-order sensitivity of a plug-in poststratified estimand to that of a weighted average of fitted response means, with both derivatives taken with respect to the latent mean-scale vector. Simulations show that HGP achieves lower population-weighted prediction error under nonparametric structure, whereas logistic regression performs well under correct parametric specification. Additional analyses examine sample size, frame coverage, subgroup prediction, and population-mean agreement. An application to the Future of Families and Child Wellbeing Study illustrates the method. Overall, this work extends local equivalent-weight construction to nonparametric modeling and provides a computational framework and conditional theoretical results for survey weighting in structured, sparse populations.