Distributions of Posterior Quantiles via Matching

Anton Kolotilin and Alexander Wolitzky

Papers from arXiv.org

Abstract: We offer a simple analysis of the problem of choosing a statistical experiment to optimize the induced distribution of posterior medians, or more generally $q$-quantiles for any $q \in (0,1)$. We show that all implementable distributions of the posterior $q$-quantile are implemented by a single experiment, the $q$-quantile matching experiment, which pools pairs of states across the $q$-quantile of the prior in a positively assortative manner, with weight $q$ on the lower state in each pair. A dense subset of implementable distributions of posterior $q$-quantiles can be uniquely implemented by perturbing the $q$-quantile matching experiment. A linear functional is optimized over distributions of posterior $q$-quantiles by taking the optimal selection from each set of $q$-quantiles induced by the $q$-quantile matching experiment. The $q$-quantile matching experiment is the only experiment that simultaneously implements all implementable distributions of the posterior $q$-quantile.

Date: 2024-02
New Economics Papers: this item is included in nep-exp and nep-mac
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Related works:
Journal Article: Distributions of posterior quantiles via matching (2024)
Working Paper: Distributions of Posterior Quantiles via Matching (2024)
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