Biometrika最新文献

英文中文

An anomaly arising in the analysis of processes with more than one source of variability 在分析具有一个以上变率源的过程时出现的异常

IF 2.7 2区数学 Q1 Mathematics

Biometrika

Pub Date : 2023-07-18 DOI: 10.1093/biomet/asad044

H. Battey, P. McCullagh

It is frequently observed in practice that the Wald statistic gives a poor assessment of the statistical significance of a variance component. This paper provides detailed analytic insight into the phenomenon by way of two simple models, which point to an atypical geometry as the source of the aberration. The latter can in principle be checked numerically to cover situations of arbitrary complexity, such as those arising from elaborate forms of blocking in an experimental context, or models for longitudinal or clustered data. The salient point, echoing Dickey (2020), is that a suitable likelihood-ratio test should always be used for the assessment of variance components.

在实践中经常观察到Wald统计量对方差成分的统计显著性给出了很差的评估。本文通过两个简单的模型对这一现象提供了详细的分析见解，这两个模型指出非典型几何形状是像差的来源。后者原则上可以通过数值检查来涵盖任意复杂性的情况，例如在实验环境中由复杂形式的阻塞引起的情况，或者纵向或集群数据的模型。与Dickey(2020)相呼应的重点是，应该始终使用合适的似然比检验来评估方差成分。

引用次数: 0

A cross-validation-based statistical theory for point processes 基于交叉验证的点过程统计理论

IF 2.7 2区数学 Q1 Mathematics

Biometrika

Pub Date : 2023-06-27 DOI: 10.1093/biomet/asad041

O. Cronie, M. Moradi, C. Biscio

Motivated by cross-validation’s general ability to reduce overfitting and mean square error, we develop a cross-validation-based statistical theory for general point processes. It is based on the combination of two novel concepts for general point processes: cross-validation and prediction errors. Our cross-validation approach uses thinning to split a point process/pattern into pairs of training and validation sets, while our prediction errors measure discrepancy between two point processes. The new statistical approach, which may be used to model different distributional characteristics, exploits the prediction errors to measure how well a given model predicts validation sets using associated training sets. Having indicated that our new framework generalizes many existing statistical approaches, we then establish different theoretical properties for it, including large sample properties. We further recognize that non-parametric intensity estimation is an instance of Papangelou conditional intensity estimation, which we exploit to apply our new statistical theory to kernel intensity estimation. Using independent thinning-based cross-validation, we numerically show that the new approach substantially outperforms the state of the art in bandwidth selection. Finally, we carry out intensity estimation for a dataset in forestry (Euclidean domain) and a dataset in neurology (linear network).

受交叉验证减少过拟合和均方误差的一般能力的启发，我们为一般点过程开发了一种基于交叉验证的统计理论。它基于通用点过程的两个新概念的组合：交叉验证和预测误差。我们的交叉验证方法使用细化将点过程/模式划分为成对的训练集和验证集，而我们的预测误差测量两点过程之间的差异。新的统计方法可用于对不同的分布特征进行建模，利用预测误差来衡量给定模型使用相关训练集预测验证集的效果。在指出我们的新框架概括了许多现有的统计方法后，我们为它建立了不同的理论性质，包括大样本性质。我们进一步认识到，非参数强度估计是Papangelou条件强度估计的一个例子，我们利用它将我们的新统计理论应用于核强度估计。使用基于独立稀疏的交叉验证，我们在数值上表明，新方法在带宽选择方面显著优于现有技术。最后，我们对林业数据集（欧几里得域）和神经病学数据集（线性网络）进行了强度估计。

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引用次数: 0

A mark-specific quantile regression model. 特定于标记的分位数回归模型

IF 2.4 2区数学 Q2 BIOLOGY

Biometrika

Pub Date : 2023-06-20 eCollection Date: 2024-03-01 DOI: 10.1093/biomet/asad039

Lianqiang Qu, Liuquan Sun, Yanqing Sun

Quantile regression has become a widely used tool for analysing competing risk data. However, quantile regression for competing risk data with a continuous mark is still scarce. The mark variable is an extension of cause of failure in a classical competing risk model where cause of failure is replaced by a continuous mark only observed at uncensored failure times. An example of the continuous mark variable is the genetic distance that measures dissimilarity between the infecting virus and the virus contained in the vaccine construct. In this article, we propose a novel mark-specific quantile regression model. The proposed estimation method borrows strength from data in a neighbourhood of a mark and is based on an induced smoothed estimation equation, which is very different from the existing methods for competing risk data with discrete causes. The asymptotic properties of the resulting estimators are established across mark and quantile continuums. In addition, a mark-specific quantile-type vaccine efficacy is proposed and its statistical inference procedures are developed. Simulation studies are conducted to evaluate the finite sample performances of the proposed estimation and hypothesis testing procedures. An application to the first HIV vaccine efficacy trial is provided.

分位数回归已成为分析竞争风险数据的一种广泛使用的工具。然而，具有连续标记的竞争风险数据的分位数回归仍然很少。标记变量是经典竞争风险模型中失败原因的扩展，其中失败原因被仅在未经审查的失败时间观察到的连续标记所取代。连续标记变量的一个例子是测量感染病毒和疫苗构建体中所含病毒之间差异的遗传距离。在这篇文章中，我们提出了一个新的标记特定的分位数回归模型。所提出的估计方法借用了标记附近数据的强度，并基于诱导平滑估计方程，这与现有的用于具有离散原因的竞争风险数据的方法非常不同。结果估计量的渐近性质是在标记和分位数连续性上建立的。此外，还提出了一种标记特异性分位数型疫苗的有效性，并开发了其统计推断程序。进行了仿真研究，以评估所提出的估计和假设检验程序的有限样本性能。提供了第一个HIV疫苗疗效试验的应用。

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引用次数: 0

Correction to: Ancestor regression in linear structural equation models 修正：线性结构方程模型中的祖先回归

IF 2.7 2区数学 Q1 Mathematics

Biometrika

Pub Date : 2023-06-10 DOI: 10.1093/biomet/asad028

引用次数: 0

Interpolating discriminant functions in high-dimensional Gaussian latent mixtures 高维高斯潜混合中判别函数的插值

2区数学 Q1 Mathematics

Biometrika

Pub Date : 2023-06-08 DOI: 10.1093/biomet/asad037

Xin Bing, Marten Wegkamp

Abstract This paper considers binary classification of high-dimensional features under a postulated model with a low-dimensional latent Gaussian mixture structure and nonvanishing noise. A generalized least-squares estimator is used to estimate the direction of the optimal separating hyperplane. The estimated hyperplane is shown to interpolate on the training data. While the direction vector can be consistently estimated, as could be expected from recent results in linear regression, a naive plug-in estimate fails to consistently estimate the intercept. A simple correction, which requires an independent hold-out sample, renders the procedure minimax optimal in many scenarios. The interpolation property of the latter procedure can be retained, but surprisingly depends on the way the labels are encoded.

摘要本文研究了具有低维潜在高斯混合结构和非消失噪声的假设模型下高维特征的二分类问题。利用广义最小二乘估计估计了最优分离超平面的方向。用估计的超平面对训练数据进行插值。虽然方向向量可以被一致地估计，正如最近线性回归的结果所期望的那样，一个幼稚的插件估计不能一致地估计截距。一个简单的校正，它需要一个独立的保留样本，在许多情况下使程序最小化。后一个过程的插值属性可以保留，但令人惊讶的是，这取决于标签编码的方式。

引用次数: 1

Sample-constrained partial identification with application to selection bias. 应用于选择偏差的样本约束部分识别。

IF 2.7 2区数学 Q1 Mathematics

Biometrika

Pub Date : 2023-06-01 DOI: 10.1093/biomet/asac042

Matthew J Tudball, Rachael A Hughes, Kate Tilling, Jack Bowden, Qingyuan Zhao

Many partial identification problems can be characterized by the optimal value of a function over a set where both the function and set need to be estimated by empirical data. Despite some progress for convex problems, statistical inference in this general setting remains to be developed. To address this, we derive an asymptotically valid confidence interval for the optimal value through an appropriate relaxation of the estimated set. We then apply this general result to the problem of selection bias in population-based cohort studies. We show that existing sensitivity analyses, which are often conservative and difficult to implement, can be formulated in our framework and made significantly more informative via auxiliary information on the population. We conduct a simulation study to evaluate the finite sample performance of our inference procedure, and conclude with a substantive motivating example on the causal effect of education on income in the highly selected UK Biobank cohort. We demonstrate that our method can produce informative bounds using plausible population-level auxiliary constraints. We implement this method in the [Formula: see text] package [Formula: see text].

许多部分辨识问题的特征是函数在集合上的最优值，其中函数和集合都需要由经验数据估计。尽管在凸问题上取得了一些进展，但在这种一般情况下的统计推断仍有待发展。为了解决这个问题，我们通过对估计集进行适当的松弛，推导出最优值的渐近有效置信区间。然后，我们将这一一般结果应用于基于人群的队列研究中的选择偏倚问题。我们表明，现有的敏感性分析往往是保守的，难以实施，可以在我们的框架中制定，并通过对人口的辅助信息使信息更加丰富。我们进行了一项模拟研究，以评估我们的推理过程的有限样本性能，并以一个实质性的激励例子来总结教育对收入的因果影响，这个例子是在高度选择的英国生物银行队列中进行的。我们证明了我们的方法可以使用合理的人口水平辅助约束产生信息界。我们在[Formula: see text]包[Formula: see text]中实现了这个方法。

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引用次数: 4

Bayesian learning of network structures from interventional experimental data 基于介入实验数据的网络结构贝叶斯学习

IF 2.7 2区数学 Q1 Mathematics

Biometrika

Pub Date : 2023-05-11 DOI: 10.1093/biomet/asad032

F. Castelletti, S. Peluso

Directed Acyclic Graphs (DAGs) provide an effective framework for learning causal relationships among variables given multivariate observations. Under pure observational data, DAGs encoding the same conditional independencies cannot be distinguished and are collected into Markov equivalence classes. In many contexts however, observational measurements are supplemented by interventional data that improve DAG identifiability and enhance causal effect estimation. We propose a Bayesian framework for multivariate data partially generated after stochastic interventions. To this end, we introduce an effective prior elicitation procedure leading to a closed-form expression for the DAG marginal likelihood and guaranteeing score equivalence among DAGs that are Markov equivalent post intervention. Under the Gaussian setting we show, in terms of posterior ratio consistency, that the true network will be asymptotically recovered, regardless of the specific distribution of the intervened variables and of the relative asymptotic dominance between observational and interventional measurements. We validate our theoretical results in simulation and we implement on both synthetic and biological protein expression data a Markov chain Monte Carlo sampler for posterior inference on the space of DAGs.

有向无环图(dag)提供了一个有效的框架来学习变量之间的因果关系给定的多变量观察。在纯观测数据下，无法区分编码相同条件独立性的dag，并将其收集到马尔可夫等价类中。然而，在许多情况下，通过干预数据补充观察测量，可提高DAG的可识别性并增强因果效应估计。我们提出了一个贝叶斯框架，用于随机干预后部分生成的多变量数据。为此，我们引入了一个有效的先验启发程序，导致DAG边际似然的封闭形式表达式，并保证干预后马尔可夫等效DAG之间的分数相等。在高斯设置下，根据后验比一致性，我们表明，无论干预变量的具体分布以及观察和干预测量之间的相对渐近优势如何，真实网络都将渐近恢复。我们在模拟中验证了我们的理论结果，并在合成和生物蛋白表达数据上实现了一个马尔可夫链蒙特卡罗采样器，用于对dag空间的后验推理。

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引用次数: 1

Populations of Unlabelled Networks: Graph Space Geometry and Generalized Geodesic Principal Components 未标记网络的总体:图空间几何和广义测地线主成分

IF 2.7 2区数学 Q1 Mathematics

Biometrika

Pub Date : 2023-04-04 DOI: 10.1093/biomet/asad024

Anna Calissano, Aasa Feragen, S. Vantini

Statistical analysis for populations of networks is widely applicable but challenging as networks have strongly non-Euclidean behaviour. Graph space is an exhaustive framework for studying populations of unlabelled networks which are weighted or unweighted, uni- or multi-layered, directed or undirected. Viewing graph space as the quotient of a Euclidean space with respect to a finite group action, we show that it is not a manifold, and that its curvature is unbounded from above. Within this geometrical framework we define generalized geodesic principal components, and we introduce the align all and compute algorithms, all of which allow for the computation of statistics on graph space. The statistics and algorithms are compared with existing methods and empirically validated on three real datasets, showcasing the framework potential utility. The whole framework is implemented within the geomstats Python package.

网络总体的统计分析是广泛适用的，但具有挑战性，因为网络具有强烈的非欧几里德行为。图空间是一个详尽的框架，用于研究加权或未加权、单层或多层、有向或无向的未标记网络的种群。将图空间看作欧几里得空间相对于有限群作用的商，我们证明了它不是流形，并且它的曲率从上看是无界的。在这个几何框架内，我们定义了广义测地线主分量，并引入了align all和compute算法，所有这些算法都允许在图空间上计算统计信息。将统计数据和算法与现有方法进行了比较，并在三个真实数据集上进行了实证验证，展示了框架的潜在效用。整个框架是在geomstats Python包中实现的。

引用次数: 3

Scalable subsampling: computation, aggregation and inference 可伸缩子抽样:计算、聚合和推理

2区数学 Q1 Mathematics

Biometrika

Pub Date : 2023-03-21 DOI: 10.1093/biomet/asad021

Dimitris N Politis

Abstract Subsampling has seen a resurgence in the big data era where the standard, full-resample size bootstrap can be infeasible to compute. Nevertheless, even choosing a single random subsample of size b can be computationally challenging with both b and the sample size n being very large. This paper shows how a set of appropriately chosen, nonrandom subsamples can be used to conduct effective, and computationally feasible, subsampling distribution estimation. Furthermore, the same set of subsamples can be used to yield a procedure for subsampling aggregation, also known as subagging, that is scalable with big data. Interestingly, the scalable subagging estimator can be tuned to have the same, or better, rate of convergence than that of θ^n. Statistical inference could then be based on the scalable subagging estimator instead of the original θ^n.

在大数据时代，由于标准的、全样本大小的bootstrap可能无法计算，子抽样已经重新兴起。然而，即使选择大小为b的单个随机子样本，在b和样本量n都非常大的情况下，也可能在计算上具有挑战性。本文展示了如何使用一组适当选择的非随机子样本进行有效且计算可行的子抽样分布估计。此外，同一组子样本可用于产生子样本聚合过程，也称为subagging，该过程可与大数据一起扩展。有趣的是，可伸缩subagging估计器可以被调整为具有与θ^n相同或更好的收敛率。统计推断可以基于可扩展subagging估计器而不是原始的θ^n。

引用次数: 0

Causal inference with misspecified exposure mappings: separating definitions and assumptions 具有错误指定暴露映射的因果推断：分离定义和假设

IF 2.7 2区数学 Q1 Mathematics

Biometrika

Pub Date : 2023-03-16 DOI: 10.1093/biomet/asad019

F. Sävje

Exposure mappings facilitate investigations of complex causal effects when units interact in experiments. Current methods require experimenters to use the same exposure mappings both to define the effect of interest and to impose assumptions on the interference structure. However, the two roles rarely coincide in practice, and experimenters are forced to make the often questionable assumption that their exposures are correctly specified. This paper argues that the two roles exposure mappings currently serve can, and typically should, be separated, so that exposures are used to define effects without necessarily assuming that they are capturing the complete causal structure in the experiment. The paper shows that this approach is practically viable by providing conditions under which exposure effects can be precisely estimated when the exposures are misspecified. Some important questions remain open.

当单元在实验中相互作用时，暴露映射有助于研究复杂的因果效应。目前的方法要求实验者使用相同的暴露映射来定义感兴趣的效果，并对干扰结构进行假设。然而，在实践中，这两个角色很少重合，实验者被迫做出一个经常令人怀疑的假设，即他们的暴露是正确的。本文认为，暴露映射目前所服务的两个角色可以而且通常应该分开，这样暴露就可以用来定义效应，而不必假设它们在实验中捕捉到了完整的因果结构。该论文表明，这种方法在实际中是可行的，因为它提供了一些条件，在这些条件下，当暴露被错误指定时，可以精确估计暴露效应。一些重要问题仍然悬而未决。

引用次数: 1

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