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Abstract:
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We present a Bayesian framework for estimating population parameters with matched samples. Our approach begins by introducing a latent matching structure, namely, a binary matrix C with constraints on the margins. We further posit a likelihood for the relationship between the matching variables. A Bayesian analysis of the matched samples then corresponds to drawing from the joint posterior distribution of C and the parameters. We describe algorithms for posterior sampling of many different matching structures. We consider one-to-one, as well as one-to-many matching. In addition, we vary the size of the matched set to satisfy analyst-specified distance constraints, and obtain a maximum-cardinality bipartite matching. We also allow for matching with replacement, i.e., we let a donor unit be used as a potential match multiple times. We show how our framework: (i) enables connecting well-known Bayesian methods, such as the Bayesian bootstrap, to the statistical matching paradigm, and (ii) allows for inclusion of many commonly used matching techniques. Empirical studies demonstrate that our approach can accurately quantify uncertainty in parameter estimates obtained from matched data.
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