Bayesian Nonparameteric Multiresolution Estimation for the American Community Survey

TL;DR

This paper introduces a Bayesian multiresolution approach for small area estimation that leverages observations across multiple spatial and temporal scales to improve accuracy in estimating county-level employment from the American Community Survey.

Contribution

It develops a novel Bayesian multiresolution model using Gaussian process mixtures and a modified Dirichlet process prior for improved small area estimation.

Findings

Enhanced estimation accuracy demonstrated on synthetic data

Effective integration of multi-scale observations in real data

Flexible nonparametric modeling of county-level employment

Abstract

Bayesian hierarchical methods implemented for small area estimation focus on reducing the noise variation in published government official statistics by borrowing information among dependent response values. Even the most flexible models confine parameters defined at the finest scale to link to each data observation in a one-to-one construction. We propose a Bayesian multiresolution formulation that utilizes an ensemble of observations at a variety of coarse scales in space and time to additively nest parameters we define at a finer scale, which serve as our focus for estimation. Our construction is motivated by and applied to the estimation of $1-$ year period employment levels, indexed by county, from statistics published at coarser areal domains and multi-year intervals in the American Community Survey (ACS). We construct a nonparametric mixture of Gaussian processes as the prior on a set of regression coefficients of county-indexed latent functions over multiple survey years. We evaluate a modified Dirichlet process prior that incorporates county-year predictors as the mixing measure. Each county-year parameter of a latent function is estimated from multiple coarse scale observations in space and time to which it links. The multiresolution formulation is evaluated on synthetic data and applied to the ACS.