From Blackwell Dominance in Large Samples to Renyi Divergences and Back Again

Xiaosheng Mu, Luciano Pomatto, Philipp Strack () and Omer Tamuz

Papers from arXiv.org

Abstract: We study repeated independent Blackwell experiments; standard examples include drawing multiple samples from a population, or performing a measurement in different locations. In the baseline setting of a binary state of nature, we compare experiments in terms of their informativeness in large samples. Addressing a question due to Blackwell (1951), we show that generically an experiment is more informative than another in large samples if and only if it has higher Renyi divergences. We apply our analysis to the problem of measuring the degree of dissimilarity between distributions by means of divergences. A useful property of Renyi divergences is their additivity with respect to product distributions. Our characterization of Blackwell dominance in large samples implies that every additive divergence that satisfies the data processing inequality is an integral of Renyi divergences.

Date: 2019-06, Revised 2020-09
New Economics Papers: this item is included in nep-exp and nep-mic
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Citations: View citations in EconPapers (7)

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Journal Article: From Blackwell Dominance in Large Samples to Rényi Divergences and Back Again (2021)
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Persistent link: https://EconPapers.repec.org/RePEc:arx:papers:1906.02838

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