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秩变换子抽样：多次数据拆分与可交换 p 值的推断AI 解读

Abstract Many testing problems are readily amenable to randomized tests, such as those employing data splitting. However, despite their usefulness in principle, randomized tests have obvious drawbacks. Firstly, two analyses of the same dataset may lead to different results. Secondly, the test typically loses power because it does not fully utilize the entire sample. As a remedy to these drawbacks, we study how to combine the test statistics or p-values resulting from…

连续索引图模型AI 解读

Abstract Let X={Xu}u∈U be a real-valued Gaussian process indexed by a set U. We show that X can be viewed as a graphical model with an uncountably infinite graph, where each Xu is a vertex. This graph is characterized by the reproducing property of X’s covariance kernel, without restricting U to be finite or countable, allowing the modelling of stochastic processes in continuous time/space. Unlike traditional methods, this characterization is not based on zero entries of an…

通过随机游走转移耦合对齐与比较有向网络AI 解读

Abstract We describe and study a transport-based procedure called network optimal transition coupling (NetOTC) for the comparison and alignment of two networks. The networks of interest may be directed or undirected, weighted or unweighted, and may have distinct vertex sets of different sizes. Given two networks and a cost function relating their vertices, NetOTC finds a transition coupling of their associated random walks having minimum expected cost. The minimizing cost…

按模态的主子空间追踪与矩阵尖峰协方差模型AI 解读

Abstract This paper introduces a novel framework called Mode-wise Principal Subspace Pursuit (MOP-UP) to extract hidden variations in both the row and column dimensions for matrix data. To enhance the understanding of the framework, we introduce a class of matrix-variate spiked covariance models that serve as inspiration for the development of the MOP-UP algorithm. The MOP-UP algorithm consists of two steps: Average Subspace Capture (ASC) and Alternating Projection. These…

扩展信赖推断：迈向自动化统计推断AI 解读

Abstract While fiducial inference was widely considered a big blunder by R.A. Fisher, the goal he initially set—‘inferring the uncertainty of model parameters on the basis of observations’—has been continually pursued by many statisticians. To this end, we develop a new statistical inference method called extended Fiducial inference (EFI). The new method achieves the goal of fiducial inference by leveraging advanced statistical computing techniques while remaining scalable…

连续时间生存与事件史分析中边际因果效应识别的图形准则AI 解读

Abstract We consider continuous-time survival and event-history settings, where our aim is to graphically represent causal structures allowing us to characterize when a causal parameter is identified from observational data. This causal parameter is formalized as the effect on an outcome event of a (possibly hypothetical) intervention on the intensity of a treatment process. To establish identifiability, we propose novel graphical rules indicating whether the observed…

捕捉信号：利用 knockoff e 值进行信号定位AI 解读

Abstract We consider problems where many, somewhat redundant, hypotheses are tested and we are interested in reporting the most precise rejections, with false discovery rate (FDR) control. This is the case, for example, when researchers are interested both in individual hypotheses as well as group hypotheses corresponding to intersections of sets of the original hypotheses, at several resolution levels. A concrete application is in genome-wide association studies, where,…

协变量调整回归函数的去偏推断AI 解读

Abstract In this article, we study nonparametric inference for a covariate-adjusted regression function. This parameter captures the average association between a continuous exposure and an outcome after adjusting for other covariates. Under certain causal conditions, it also corresponds to the average outcome had all units been assigned to a specific exposure level, known as the causal dose–response curve. We propose a debiased local linear estimator of the…

通过非参数极大似然实现多元异方差经验贝叶斯估计AI 解读

Abstract Multivariate, heteroscedastic errors complicate statistical inference in many large-scale denoizing problems. Empirical Bayes is attractive in such settings, but standard parametric approaches rest on assumptions about the form of the prior distribution which can be hard to justify and which introduce unnecessary tuning parameters. We extend the nonparametric maximum-likelihood estimator (NPMLE) for Gaussian location mixture densities to allow for multivariate,…

Wenkai Xu 对《安全检验》的讨论AI 解读

The authors propose the framework of e-value testing by investigating the grow-rate-optimal (GRO) constructions of e-variables, that incorporate a comprehensive range of testing scenarios for simple alternative, as well as their composite counterparts. The authors illustrate the versatility of e-value tests via three interpretations, drawing connections to (1) game-theoretical viewpoint, (2) conservative p-values, and (3) Bayes Factors; and devise the determination and…

Judith ter Schure 对《安全检验》的讨论AI 解读

Once there was a randomized controlled trial (RCT) that studied the recurrence of stroke. It had assumed for the treatment of interest a 40% reduction in hazard, and had set the sample size accordingly (Kamel et al., 2024). The RCT found a 95% confidence interval of (−55%, 36%) and concluded no statistical significance. ‘Absence of evidence is not evidence of absence’ said the statisticians (Altman & Bland, 1995; Harrell, 2024). But the story goes that the sample size was…

Pace 与 Salvan 对《安全检验》的讨论贡献AI 解读

We wish to congratulate the authors on their important paper. In this contribution, we will focus on parametric models, where e-values provide a welcome new perspective on likelihood ratios and Bayes factors, as well as a useful addition to the discussion about the foundational concept of statistical evidence. The guarantees sought for in safe testing are frequentist, but prior information may be injected in Bayesian terms, establishing an alliance between traditionally…

Christine P. Chai 对《安全检验》的讨论AI 解读

This paper proposes the e-value for ‘safe testing’ as an alternative to the p-value in hypothesis testing. The e-value allows for optional continuation while preserving Type-I error guarantees. I hope to see lots of discussion at the Royal Statistical Society meeting, like the previous ‘Signs and sizes: Understanding and replicating statistical findings’ (Hutton et al., 2020). I have some questions regarding the descriptions: I see some comparisons between the e-value and…

田茂再、余克明与王江峰对《安全检验》的讨论AI 解读

We want to congratulate the authors on the publication of ‘Safe Testing’ on JRSS-B. It deepens our understanding of the statistical hypothesis test that is one particular method of statistical inference used to decide whether the data sufficiently support a particular hypothesis. The e-variables and safe tests offer several advantages. The authors develop the theory of hypothesis testing based on the e-value that behave excellently under optional continuation and are…

Joris Mulder 对《安全检验》的讨论评论AI 解读

The potential of e-values (or e-variables) to unite different schools of statistics and allowing optional stopping/continuation in a ‘safe’ manner is a major accomplishment of the authors. The theory implies a change in focus from classical error rates to the expected evidence against the null under the respective hypotheses. Under H0⁠, it is required that the expectation of the evidence against the null, E, should not exceed 1, i.e. EH0[E]≤1⁠, as in formula (1) of ‘Safe…

Christian Hennig对《安全检验》的讨论AI 解读

I appreciate the elegance of the theory regarding (RE)GRO(W) e-variables with optional continuation for combining evidence. Here are some rather problematic aspects. (1) The authors state that ‘there seems to be growing consensus that, in the context of hypothesis testing, p-values should either not be used at all, or at least, with utter care’. I see little consensus that p-values should not be used at all. The request for ‘utter care’ is sensible, but I do not believe that…

Alexander Ly对《安全检验》的讨论意见AI 解读

The article by Grünwald, de Heide, and Koolen not only presents a comprehensive approach to anytime-valid testing but also offers profound insights and inspiration for statistical practice. However, there is a potential inconvenience in cases where achieving gro(w) optimality necessitates the use of point priors. In these instances, the specified point of the point prior never vanishes from the associated anytime-valid confidence interval, and it prohibits powerful…

Robert 与 Bon 对《安全检验》的讨论意见AI 解读

Central to our interest in Bayesian foundations and reference priors, the connection made in this paper between e-values and Bayes factors, despite the cautionary added label of an ‘Almost Bayesian Case’, could bring a formal way to define least favourable priors (Berger, 1985) in a testing environment, albeit in no clear connection with the reference priors of Bayarri and Garcia-Donato (2007). This derivation, formalized as Theorem 1, provides a reversal of the typical…

Joshua Bon与Christian P. Robert对《安全检验》的讨论AI 解读

The central proposal found in this quite original paper could prove relevant for the so-called objective Bayes approach (Berger, 1985; Robert, 2001) as it may open a way to deriving prior distributions from (frequentist) first principles. While some Bayesian schools refuse to consider the concept of testing the veracity of a null hypothesis, most do propose approaches and methodologies to address this challenge. These mainly rely on Jeffreys’ formalization via two prior…

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…

Dey、Martin 与 Williams 对《安全检验》的讨论贡献AI 解读

Congratulations to Grünwald, de Heide, and Koolen (GHK) for their contribution to the exciting and rapidly growing literature on safe/anytime-valid inference. GHK’s proposal focused on problems in which a statistical model is available that determines the quantity of interest—the model parameter—and provides a likelihood function that drives the e-value construction. When data are observed and analysed sequentially, however, the data analyst typically cannot say with any…

Larsson、Ramdas 与 Ruf 对《安全检验》的讨论AI 解读

We congratulate the authors on a stimulating article that has inspired many follow-up works. We discuss the central concept of growth-rate optimality (GRO). For a point null and alternative, the GRO e-variable is their likelihood ratio (Shafer, 2021). The generalization to composite nulls takes centre stage in Grünwald et al. (2024). Their use of the reverse information projection (RIPr) builds on Li (1999), and has been recently extended in Lardy et al. (2023). Inspired by…

相关性调整的去偏 Lasso：协变量模型不准确时的去偏AI 解读

Abstract We consider the problem of estimating a low-dimensional parameter in high-dimensional linear regression. Constructing an approximately unbiased estimate of the parameter of interest is a crucial step towards performing statistical inference. Several authors suggest to orthogonalize both the variable of interest and the outcome with respect to the nuisance variables, and then regress the residual outcome with respect to the residual variable. This is possible if the…

神经网络与随机森林的融合AI 解读

Abstract Neural networks and random forests are popular and promising tools for machine learning. This article explores the proper integration of these two approaches for nonparametric regression to improve the performance of a single approach. Specifically, we propose a neural network estimator with local enhancement provided by random forests. It naturally synthesizes the local relation adaptivity of random forests and the strong global approximation ability of neural…