Distributions of posterior quantiles via matching
研究了如何选择统计实验来优化后验中位数或q分位数的分布，发现q分位数匹配实验能实现所有可实现的分布，且通过扰动可唯一实现稠密子集。
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 ∈ (0,1). We show that a single experiment—the q ‐quantile matching experiment—implements all implementable distributions of posterior q ‐quantiles, with different distributions spanned by different selections from the sets of posterior q ‐quantiles. 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 posterior q ‐quantiles. The q ‐quantile matching experiment is the only experiment that simultaneously implements all implementable distributions of posterior q ‐quantiles.