From Blackwell Dominance in Large Samples to Rényi Divergences and Back Again
研究了重复独立布莱克威尔实验在大样本下的信息比较，证明一个实验比另一个更有效当且仅当其雷尼散度更高，并将此应用于分布差异度量。
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 Rényi divergences. We apply our analysis to the problem of measuring the degree of dissimilarity between distributions by means of divergences. A useful property of Rényi 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 Rényi divergences.