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Abstract:
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Bayesian models are increasingly employed by the U.S. Bureau of Labor Statistics (BLS) to render statistics, such as total employment, because these models readily account for structural dependencies in the data and estimate the full distribution from which variance estimates are computed. The estimation of posterior distributions is, however, computationally expensive. BLS collects data under informative sampling designs that assign probabilities of inclusion to be correlated with the response and induce a dependence among sampled observations. This article extends a computationally-scalable approach by composing the barycenter for a collection of pseudo posterior distributions estimated on disjoint subsets of the full data in the Wasserstein space. The extension generalizes the idea of stochastic approximation to calibrate uncertainty estimation on subset likelihoods by incorporating sampling weights. We construct conditions on known marginal and pairwise inclusion probabilities that define a class of sampling designs where consistency of the barycenter pseudo distribution is achieved. We demonstrate the result on an application to the Current Employment Statistics survey.
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