A Computationally Efficient Approach to Fully Bayesian Benchmarking
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In small area estimation, it is often necessary to resort to model-based methods in order to produce estimates in areas with little or no data. In many settings, we require that some aggregate of small area estimates agree with a national level estimate that may be considered more reliable, for internal consistency purposes. The process of enforcing this agreement is referred to as benchmarking, and while methods currently exist to perform benchmarking in many settings, few are ideal for applications with non-normal outcomes and many are computationally inefficient. Fully Bayesian benchmarking is a theoretically appealing approach insofar as we can obtain posterior distributions conditional on a benchmarking constraint. However, existing implementations are often computationally prohibitive. In this paper, we summarize existing benchmarking methods and their shortcomings in the setting of small area estimation with binary outcomes, and propose an approach in which an unbenchmarked method that produces samples can be combined with a rejection sampler to produce fully Bayesian benchmarked estimates in a computationally efficient way. To illustrate our approach, we provide comparisons of various benchmarking methods in applications to HIV prevalence and under-5 mortality estimation. Code implementing our methodology is available in the R package simultBench.
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