摘要翻译:
我们研究重复独立的布莱克威尔实验;标准示例包括从总体中提取多个样本,或在不同位置执行测量。在二元自然状态的基线设置中,我们比较实验在大样本中的信息量。针对Blackwell(1951)提出的一个问题,我们证明了在大样本条件下,一个实验比另一个实验具有更多的信息当且仅当它具有更高的Renyi散度。我们将我们的分析应用于用发散量测量分布之间的相异程度的问题。Renyi发散的一个有用性质是它们关于乘积分布的可加性。我们对大样本中Blackwell优势的刻画表明,满足数据处理不等式的加性散度都是Renyi散度的积分。
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英文标题:
《From Blackwell Dominance in Large Samples to Renyi Divergences and Back
Again》
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作者:
Xiaosheng Mu, Luciano Pomatto, Philipp Strack, and Omer Tamuz
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最新提交年份:
2020
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分类信息:
一级分类:Mathematics 数学
二级分类:Statistics Theory 统计理论
分类描述:Applied, computational and theoretical statistics: e.g. statistical inference, regression, time series, multivariate analysis, data analysis, Markov chain Monte Carlo, design of experiments, case studies
应用统计、计算统计和理论统计:例如统计推断、回归、时间序列、多元分析、数据分析、马尔可夫链蒙特卡罗、实验设计、案例研究
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一级分类:Economics 经济学
二级分类:Theoretical Economics 理论经济学
分类描述:Includes theoretical contributions to Contract Theory, Decision Theory, Game Theory, General Equilibrium, Growth, Learning and Evolution, Macroeconomics, Market and Mechanism Design, and Social Choice.
包括对契约理论、决策理论、博弈论、一般均衡、增长、学习与进化、宏观经济学、市场与机制设计、社会选择的理论贡献。
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一级分类:Mathematics 数学
二级分类:Probability 概率
分类描述:Theory and applications of probability and stochastic processes: e.g. central limit theorems, large deviations, stochastic differential equations, models from statistical mechanics, queuing theory
概率论与随机过程的理论与应用:例如中心极限定理,大偏差,随机微分方程,统计力学模型,排队论
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一级分类:Statistics 统计学
二级分类:Statistics Theory 统计理论
分类描述:stat.TH is an alias for math.ST. Asymptotics, Bayesian Inference, Decision Theory, Estimation, Foundations, Inference, Testing.
Stat.Th是Math.St的别名。渐近,贝叶斯推论,决策理论,估计,基础,推论,检验。
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英文摘要:
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.
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PDF链接:
https://arxiv.org/pdf/1906.02838