Entropic tilting (ET) is a Bayesian decision-analytic method for constraining distributions to satisfy defined targets or bounds for sets of expectations. This report recapitulates the foundations and basic theory of ET for conditioning predictive distributions on such constraints, recognising the increasing interest in ET in several application areas. Contributions include new results related to connections with regular exponential families of distributions, and the extension of ET to relaxed entropic tilting (RET) where specified values for expectations define bounds rather than exact targets. Additional new developments include theory and examples that condition on quantile constraints for modified predictive distributions and examples relevant to Bayesian forecasting applications.
翻译：环境倾斜(ET)是贝叶西亚决定分析方法,用于限制分配以满足既定目标或一系列期望的界限,本报告概述了环境倾斜(ET)的基础和基本理论,以调整预测分布时对这种限制因素的制约,承认对环境倾斜(ET)在若干应用领域的兴趣日益增加,贡献包括与正常分布指数成份的联系有关的新结果,以及将环境倾斜(RET)扩大到放松的热带倾斜(RET),其中对期望的具体值界定了界限而不是确切的目标;其他新的发展包括以修改预测分布的量化限制为条件的理论和实例,以及与贝叶西亚预测应用相关的实例。
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