A Computationally Efficient Approach to Fully Bayesian Benchmarking

TL;DR

This paper introduces a computationally efficient Bayesian benchmarking method for small area estimation with binary outcomes and uncertain benchmarks, improving consistency with national estimates while maintaining practicality.

Contribution

It proposes a novel approach combining unbenchmarked methods with rejection sampling or MCMC for efficient Bayesian benchmarking in complex, real-world applications.

Findings

Method is computationally efficient compared to existing approaches.

Demonstrated effectiveness in HIV prevalence and under-5 mortality estimation.

Provides flexible implementation with available R package.

Abstract

In small area estimation, it is sometimes necessary to use model-based methods to produce estimates in areas with little or no data. In official statistics, we often require that some aggregate of small area estimates agree with a national estimate for internal consistency purposes. Enforcing this agreement is referred to as benchmarking, and while methods currently exist to perform benchmarking, few are ideal for applications with non-normal outcomes and benchmarks with uncertainty. Fully Bayesian benchmarking is a theoretically appealing approach insofar as we can obtain posterior distributions conditional on a benchmarking constraint. However, existing implementations may be computationally prohibitive. In this paper, we critically review benchmarking methods in the context of small area estimation in low- and middle-income countries with binary outcomes and uncertain benchmarks, and propose a novel approach in which an unbenchmarked method that produces area-level samples can be combined with a rejection sampler or Metropolis-Hastings algorithm to produce benchmarked posterior distributions in a computationally efficient way. To illustrate the flexibility and efficiency of our approach, we provide comparisons to an existing benchmarking approach in a simulation, and applications to HIV prevalence and under-5 mortality estimation. Code implementing our methodology is available in the R package stbench.