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Vladimir Vovk 对《安全检验》的讨论意见AI 解读

The main result of this paper (Theorem 1) is elegant and satisfying, but in this comment I will concentrate on one of its limitations, namely the condition infW0D(Q‖PW0)<∞⁠. (Analogous conditions are present in all generalizations given in the paper.) Even in the toy binary case with an infinite horizon, this condition is typically violated. Consider, e.g., the case of Markov alternative hypotheses Q considered in Ramdas et al. (2022): a nonIID Markov probability measure (or…

任意依赖下合并p值的可容许方法AI 解读

Methods of merging several p-values into a single p-value are important in their own right and widely used in multiple hypothesis testing. This paper is the first to systematically study the admissibility (in Wald’s sense) of p-merging functions and their domination structure, without any information on the dependence structure of the input p-values. As a technical tool, we use the notion of e-values, which are alternatives to p-values recently promoted by several authors.…

通过平均值合并 p 值AI 解读

Summary This paper proposes general methods for the problem of multiple testing of a single hypothesis, with a standard goal of combining a number of $p$-values without making any assumptions about their dependence structure. A result by Rüschendorf (1982) and, independently, Meng (1993) implies that the $p$-values can be combined by scaling up their arithmetic mean by a factor of 2, and no smaller factor is sufficient in general. A similar result by Mattner about the…

在线预测线性回归AI 解读

We consider the on-line predictive version of the standard problem of linear regression; the goal is to predict each consecutive response given the corresponding explanatory variables and all the previous observations. The standard treatment of prediction in linear regression analysis has two drawbacks: (1) the classical prediction intervals guarantee that the probability of error is equal to the nominal significance level ɛ, but this property per se does not imply that the…

总能实现良好的随机化序贯概率预测AI 解读

Summary Building on the game theoretic framework for probability, we show that it is possible, using randomization, to make sequential probability forecasts that will pass any given battery of statistical tests. This result, an easy consequence of von Neumann's minimax theorem, simplifies and generalizes work by earlier researchers.