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Huk、Pacchiardi、Dutta 与 Steel 对《鞅后验分布》的讨论AI 解读

We congratulate the authors for this thought-provoking paper. The recursive definition of the predictive distributions through a bivariate copula (Section 4) depends on a hyperparameter ρ, which the authors tune by minimising the prequential log-score −∑i=1nlogpi−1(yi) (Section 4.5.2). The prequential framework nicely connects with the predictive resampling approach used later. However, other strictly proper scoring rules (Gneiting & Raftery, 2007) could be used in place of…

用于稀疏贝叶斯推断的快速异步 MCMC 采样器AI 解读

Abstract We propose a very fast approximate Markov chain Monte Carlo sampling framework that is applicable to a large class of sparse Bayesian inference problems. The computational cost per iteration in several regression models is of order O(n(s+J)), where n is the sample size, s is the underlying sparsity of the model, and J is the size of a randomly selected subset of regressors. This cost can be further reduced by data sub-sampling when stochastic gradient Langevin…

Draper 与 Guo 对《鞅后验分布》的讨论AI 解读

We have two comments motivated by this interesting paper. The idea, introduced early in the paper, that ‘the object of interest is fully defined once all the observations have been viewed’ is almost exactly 100 years old: it was a cornerstone of the remarkable paper by Fisher (1922) and has been referred to for many decades as Fisher consistency. We are surprised that the authors did not make this connection. Theorem (Draper & Guo, 2023) Under the conditions detailed above,…

布莱克·莫亚对《鞅后验分布》的讨论意见AI 解读

I would like to congratulate the authors on an expository and intuitive representation of statistical uncertainty. To assist in the further investigation of predictive resampling techniques, I have developed a software package for R (R Core Team, 2022) which implements some of the algorithms presented here as well as from subsequent work (Moya & Walker, 2023). The CopRe package (Moya, 2022), named for the copula resampling technique described in Section 4, can be installed…

贾琦顾与郭胜尹对《鞅后验分布》的讨论AI 解读

We congratulate the authors for their thought-provoking paper, especially in the three aspects as follows. Instead of imposing a prior π(θ) on the parameter θ of a likelihood function fθ(y)⁠, where both π and fθ are elicited subjectively, the authors proposed the framework of martingale posterior to directly model the predictive p(yn+1:∞∣y1:n) for which only the prior predictive p(y) needs to be specified. As a result, Bayesian inference can be conducted on any parameter (or…

Pietro Rigo 对《鞅后验分布》的讨论AI 解读

This paper is really interesting and offers a number of intriguing hints. Here, I just make a few isolated remarks without any claim of being exhaustive. I would give more emphasis to the Ionescu-Tulcea theorem (ITT). This theorem is quoted only in passing, but it is the cornerstone of this paper. By ITT, the distribution of Y1:∞=(Y1,Y2,…) is completely determined by the assignment of {Pn:n≥0}⁠, where P0(⋅)=P(Y1∈⋅) and Pn(⋅)=P(Yn+1∈⋅∣Y1:n)⁠. Exploiting ITT has at least two…

超越尖锐零假设的随机化推断：有界零假设与个体处理效应分位数AI 解读

Abstract Randomisation inference (RI) is typically interpreted as testing Fisher’s ‘sharp’ null hypothesis that all unit-level effects are exactly zero. This hypothesis is often criticised as restrictive and implausible, making its rejection scientifically uninteresting. We show, however, that many randomisation tests are also valid for a ‘bounded’ null hypothesis under which the unit-level effects are all non-positive (or all non-negative) but are otherwise heterogeneous.…

Maxway CRT：提高 model-X 推断的稳健性AI 解读

Abstract The model-X conditional randomisation test (CRT) is a flexible and powerful testing procedure for testing the hypothesis X⫫Y∣Z. However, it requires perfect knowledge of X∣Z and may lose its validity when there is an error in modelling X∣Z. This problem is even more severe when Z is of high dimensionality. In response to this, we propose the Maxway CRT, which learns the distribution of Y∣Z and uses it to calibrate the resampling distribution of X to gain robustness…

StarTrek：控制错误发现率的组合变量选择AI 解读

Variable selection on the large-scale networks has been extensively studied in the literature. While most of the existing methods are limited to the local functionals especially the graph edges, this paper focuses on selecting the discrete hub structures of the networks. Specifically, we propose an inferential method, called StarTrek filter, to select the hub nodes with degrees larger than a certain thresholding level in the high-dimensional graphical models and control the…

大量协变量下最优政策效应的推断AI 解读

Understanding the impact of the most effective policies or treatments on a response variable of interest is desirable in many empirical works in economics, statistics and other disciplines. Due to the widespread winner’s curse phenomenon, conventional statistical inference assuming that the top policies are chosen independent of the random sample may lead to overly optimistic evaluations of the best policies. In recent years, given the increased availability of large…

超高维数据筛选后的诊断检验AI 解读

We propose a consistent lack-of-fit test to assess whether replacing the original ultrahigh dimensional covariates with a given number of linear combinations results in a loss of regression information. To attenuate the spurious correlations that may inflate type-I error rates in high dimensions, we suggest to randomly split the observations into two parts. In the first part, we screen out as many irrelevant covariates as possible. This screening step helps to reduce the…

随机前沿分析中无效率分布设定的检验AI 解读

Stochastic frontier analysis is regularly used in empirical studies to evaluate the productivity and efficiency of companies. A typical stochastic frontier model involves a parametric frontier subject to a composite error term consisting of an inefficiency and a random error. We develop new tests for specification of distribution of the inefficiency. We focus on simultaneous relaxation of two common assumptions: (1) parametric frontier which may lead to false conclusions…

异常值引起的回归系数扭曲检验及气候变化应用AI 解读

Outlying observations can bias regression estimates, requiring the use of outlier-robust estimators. Comparing robust estimates to those obtained using ordinary least squares (OLS) is a common robustness check, however, such comparisons have been mostly informal due to the lack of available tests. Here we introduce a formal test for coefficient distortion due to outliers in regression models. Our proposed test is based on the difference between OLS and robust estimates…

阈值自回归 bootstrap 检验的有效性AI 解读

We consider bootstrap-based testing for threshold effects in non-linear threshold autoregressive (TAR) models. It is well-known that classic tests based on asymptotic theory tend to be biased in case of small, or even moderate sample sizes, especially when the estimated parameters indicate non-stationarity, or in presence of heteroskedasticity, as often witnessed in the analysis of financial or climate data. To address the issue we propose a supremum Lagrange Multiplier test…

线性时变系数模型的筛自助法推断AI 解读

We propose a sieve bootstrap framework to conduct pointwise and simultaneous inference for time-varying coefficient regression models based on a local linear estimator. The asymptotic validity of the sieve bootstrap in the presence of autocorrelation is established. The bootstrap automatically produces a consistent estimate of nuisance parameters, both at the interior and boundary points. In addition, we develop a bootstrap-based test for parameter constancy and examine its…

超越 RCP8.5：利用准代表性浓度路径评估边际减排AI 解读

Assessments of decreases in economic damages from climate change mitigation typically rely on climate output from computationally expensive pre-computed runs of general circulation models under a handful of scenarios with discretely varying targets, such as the four representative concentration pathways for CO2 and other anthropogenically emitted gases. Although such analyses are valuable in informing scientists and policymakers about massive multilateral mitigation goals,…

有序响应模型的简便半参数估计AI 解读

We propose two simple semiparametric estimation methods for ordered response models with an unknown error distribution. The proposed methods do not require users to choose any tuning parameters, and they automatically incorporate the monotonicity restriction of the unknown distribution function. Fixing finite-dimensional parameters in the model, we construct nonparametric maximum likelihood estimates for the error distribution based on the related binary choice data or the…

采用结构化尖峰厚尾先验的贝叶斯病灶估计AI 解读

Neural demyelination and brain damage accumulated in white matter appear as hyperintense areas on T2-weighted MRI scans in the form of lesions. Modeling binary images at the population level, where each voxel represents the existence of a lesion, plays an important role in understanding aging and inflammatory diseases. We propose a scalable hierarchical Bayesian spatial model, called BLESS, capable of handling binary responses by placing continuous spike-and-slab mixture…

极值估计量的自助法AI 解读

This article develops a bootstrap analogue of the well-known asymptotic expansion of the tail quantile process in extreme value theory. One application of this result is to construct confidence intervals for estimators of the extreme value index such as the Probability Weighted Moment (PWM) estimator. For the peaks-over-threshold method, we show the bootstrap consistency of the confidence intervals. By contrast, the asymptotic expansion of the quantile process of the…

基于非参数泊松混合的 Fisher–Pitman 置换检验及其单细胞基因组学应用AI 解读

This article investigates the theoretical and empirical performance of Fisher-Pitman-type permutation tests for assessing the equality of unknown Poisson mixture distributions. Building on nonparametric maximum likelihood estimators (NPMLEs) of the mixing distribution, these tests are theoretically shown to be able to adapt to complicated unspecified structures of count data and also consistent against their corresponding ANOVA-type alternatives; the latter is a result in…

基于双尺度分布近邻的最优非参数推断AI 解读

The weighted nearest neighbors (WNN) estimator has been popularly used as a flexible and easy-to-implement nonparametric tool for mean regression estimation. The bagging technique is an elegant way to form WNN estimators with weights automatically generated to the nearest neighbors (Steele, 2009; Biau et al., 2010); we name the resulting estimator as the distributional nearest neighbors (DNN) for easy reference. Yet, there is a lack of distributional results for such…

重复标记点过程中的标记与点依赖：偏差校正及检验AI 解读

Mark-point dependence plays a critical role in research problems that can be fitted into the general framework of marked point processes. In this work, we focus on adjusting for mark-point dependence when estimating the mean and covariance functions of the mark process, given independent replicates of the marked point process. We assume that the mark process is a Gaussian process and the point process is a log-Gaussian Cox process, where the mark-point dependence is…

评估对无混杂假设的敏感性：估计与推断AI 解读

This article provides a set of methods for quantifying the robustness of treatment effects estimated using the unconfoundedness assumption. Specifically, we estimate and do inference on bounds for various treatment effect parameters, like the Average Treatment Effect (ATE) and the average effect of treatment on the treated (ATT), under nonparametric relaxations of the unconfoundedness assumption indexed by a scalar sensitivity parameter c. These relaxations allow for limited…

干扰参数位于边界时的 GARCH 设定检验AI 解读

This article develops tests for the correct specification of the conditional variance function in GARCH models when the true parameter may lie on the boundary of the parameter space. The test statistics considered are of Kolmogorov-Smirnov and Cramér-von Mises type, and are based on empirical processes marked by centered squared residuals. The limiting distributions of the test statistics depend on unknown nuisance parameters in a nontrivial way, making the tests difficult…