Biometrika最新文献

英文中文

On geometric convergence for MALA under simple conditions 简单条件下MALA的几何收敛性

2区数学 Q2 BIOLOGY

Biometrika

Pub Date : 2023-10-03 DOI: 10.1093/biomet/asad060

Alain Oliviero-Durmus, Éric Moulines

Summary While the Metropolis Adjusted Langevin Algorithm (MALA) is a popular and widely used Markov chain Monte Carlo method, very few papers derive conditions that ensure its convergence. In particular, to the authors' knowledge, assumptions that are both easy to verify and guarantee geometric convergence, are still missing. In this work, we establish V-uniformly geometric convergence for MALA under mild assumptions about the target distribution. Unlike previous work, we only consider tail and smoothness conditions for the potential associated with the target distribution. These conditions are quite common in the MCMC literature. Finally, we pay special attention to the dependence of the bounds we derive on the step size of the Euler-Maruyama discretization, which corresponds to the proposal Markov kernel of MALA.

Metropolis Adjusted Langevin Algorithm (MALA)是一种广泛应用的马尔可夫链蒙特卡罗算法，但很少有论文给出保证其收敛性的条件。特别是，据作者所知，那些既容易验证又保证几何收敛的假设仍然缺失。在对目标分布的温和假设下，我们建立了MALA的v -均匀几何收敛性。与以前的工作不同，我们只考虑与目标分布相关的势的尾部和平滑条件。这些情况在MCMC文献中很常见。最后，我们特别注意了我们得到的边界与Euler-Maruyama离散化的步长的依赖关系，这对应于MALA的建议马尔可夫核。

引用次数: 0

Efficient Evaluation of Natural Stochastic Policies in Offline Reinforcement Learning 离线强化学习中自然随机策略的有效评价

2区数学 Q2 BIOLOGY

Biometrika

Pub Date : 2023-09-27 DOI: 10.1093/biomet/asad059

Nathan Kallus, Masatoshi Uehara

We study the efficient off-policy evaluation of natural stochastic policies, which are defined in terms of deviations from the behavior policy. This is a departure from the literature on off-policy evaluation where most work consider the evaluation of explicitly specified policies. Crucially, offline reinforcement learning with natural stochastic policies can help alleviate issues of weak overlap, lead to policies that build upon current practice, and improve policies' implementability in practice. Compared with the classic case of a pre-specified evaluation policy, when evaluating natural stochastic policies, the efficiency bound, which measures the best-achievable estimation error, is inflated since the evaluation policy itself is unknown. In this paper, we derive the efficiency bounds of two major types of natural stochastic policies: tilting policies and modified treatment policies. We then propose efficient nonparametric estimators that attain the efficiency bounds under very lax conditions. These also enjoy a (partial) double robustness property.

我们研究了自然随机策略的有效离政策评估，自然随机策略是根据偏离行为策略来定义的。这与非政策评估的文献不同，在非政策评估中，大多数工作都考虑对明确规定的政策进行评估。至关重要的是，使用自然随机策略的离线强化学习可以帮助缓解弱重叠问题，产生基于当前实践的策略，并提高策略在实践中的可实施性。与经典的预先设定评估策略相比，在评估自然随机策略时，由于评估策略本身是未知的，衡量最佳可实现估计误差的效率界被夸大了。本文导出了两大类自然随机策略的效率界:倾斜策略和修正处理策略。然后我们提出有效的非参数估计，在非常宽松的条件下达到效率界。它们还具有(部分)双重鲁棒性。

引用次数: 7

Selective machine learning of doubly robust functionals 双鲁棒函数的选择性机器学习

2区数学 Q2 BIOLOGY

Biometrika

Pub Date : 2023-09-26 DOI: 10.1093/biomet/asad055

Y Cui, E Tchetgen Tchetgen

Abstract While model selection is a well-studied topic in parametric and nonparametric regression or density estimation, selection of possibly high-dimensional nuisance parameters in semiparametric problems is far less developed. In this paper, we propose a selective machine learning framework for making inferences about a finite-dimensional functional defined on a semiparametric model, when the latter admits a doubly robust estimating function and several candidate machine learning algorithms are available for estimating the nuisance parameters. We introduce a new selection criterion aimed at bias reduction in estimating the functional of interest based on a novel definition of pseudo-risk inspired by the double robustness property. Intuitively, the proposed criterion selects a pair of learners with the smallest pseudo-risk, so that the estimated functional is least sensitive to perturbations of a nuisance parameter. We establish an oracle property for a multi-fold cross-validation version of the new selection criterion which states that our empirical criterion performs nearly as well as an oracle with a priori knowledge of the pseudo-risk for each pair of candidate learners. Finally, we apply the approach to model selection of a semiparametric estimator of average treatment effect given an ensemble of candidate machine learners to account for confounding in an observational study which we illustrate in simulations and a data application.

虽然模型选择是参数和非参数回归或密度估计中一个研究得很好的主题，但半参数问题中可能高维干扰参数的选择却远远不够发达。在本文中，我们提出了一种选择性机器学习框架，用于对半参数模型上定义的有限维泛函进行推断，当后者允许双鲁棒估计函数和几种候选机器学习算法可用于估计干扰参数。基于双重鲁棒性所启发的伪风险的新定义，我们引入了一种新的选择准则，目的是在估计利息泛函时减少偏差。直观地，该准则选择了一对伪风险最小的学习器，使得估计函数对干扰参数的扰动最不敏感。我们为新选择标准的多重交叉验证版本建立了一个oracle属性，该属性表明我们的经验标准几乎与每对候选学习者的伪风险先验知识的oracle一样好。最后，我们将该方法应用于给定候选机器学习者集合的平均治疗效果的半参数估计量的模型选择，以解释我们在模拟和数据应用中说明的观察性研究中的混淆。

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引用次数: 0

An eigenvector-assisted estimation framework for signal-plus-noise matrix models 信号加噪声矩阵模型的特征向量辅助估计框架

2区数学 Q2 BIOLOGY

Biometrika

Pub Date : 2023-09-19 DOI: 10.1093/biomet/asad058

Fangzheng Xie, Dingbo Wu

Summary In this paper, we develop an eigenvector-assisted estimation framework for a collection of signal-plus-noise matrix models arising in high-dimensional statistics and many applications. The framework is built upon a novel asymptotically unbiased estimating equation using the leading eigenvectors of the data matrix. However, the estimator obtained by directly solving the estimating equation could be numerically unstable in practice and lacks robustness against model misspecification. We propose to use the quasi-posterior distribution by exponentiating a criterion function whose maximizer coincides with the estimating equation estimator. The proposed framework can incorporate heteroskedastic variance information but does not require the complete specification of the sampling distribution and is also robust to the potential misspecification of the distribution of the noise matrix. Computationally, the quasi-posterior distribution can be obtained via a Markov Chain Monte Carlo sampler, which exhibits superior numerical stability than some of the existing optimization-based estimators and is straightforward for uncertainty quantification. Under mild regularity conditions, we establish the large sample properties of the quasi-posterior distributions. In particular, the quasi-posterior credible sets have the correct frequentist nominal coverage probability provided that the criterion function is carefully selected. The validity and usefulness of the proposed framework are demonstrated through the analysis of synthetic datasets and the real-world ENZYMES network datasets.

在本文中，我们开发了一个特征向量辅助估计框架，用于高维统计和许多应用中的信号加噪声矩阵模型集合。该框架是建立在一个新的渐近无偏估计方程上，使用数据矩阵的首特征向量。然而，在实际应用中，直接求解估计方程得到的估计量在数值上是不稳定的，并且缺乏对模型错规范的鲁棒性。我们提出利用准后验分布，对一个准则函数取幂，该准则函数的最大值与估计方程估计量重合。所提出的框架可以包含异方差信息，但不需要完全规范采样分布，并且对噪声矩阵分布的潜在错误规范也具有鲁棒性。计算上，拟后验分布可以通过马尔可夫链蒙特卡罗采样器获得，与现有的一些基于优化的估计器相比，它具有更好的数值稳定性，并且可以直接用于不确定性量化。在温和的正则性条件下，我们建立了准后验分布的大样本性质。特别是，准后验可信集具有正确的频率论名义覆盖概率，前提是仔细选择准则函数。通过对合成数据集和实际酶网络数据集的分析，证明了所提出框架的有效性和实用性。

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引用次数: 0

E-values as unnormalized weights in multiple testing 在多重测试中，e值为非归一化权重

2区数学 Q2 BIOLOGY

Biometrika

Pub Date : 2023-09-15 DOI: 10.1093/biomet/asad057

Nikolaos Ignatiadis, Ruodu Wang, Aaditya Ramdas

Summary We study how to combine p-values and e-values, and design multiple testing procedures where both p-values and e-values are available for every hypothesis. Our results provide a new perspective on multiple testing with data-driven weights: while standard weighted multiple testing methods require the weights to deterministically add up to the number of hypotheses being tested, we show that this normalization is not required when the weights are e-values that are independent of the p-values. Such e-values can be obtained in meta-analysis where a primary dataset is used to compute p-values, and an independent secondary dataset is used to compute e-values. Going beyond meta-analysis, we showcase settings wherein independent e-values and p-values can be constructed on a single dataset itself. Our procedures can result in a substantial increase in power, especially if the non-null hypotheses have e-values much larger than one.

我们研究了如何结合p值和e值，并设计了多个检验程序，其中p值和e值对于每个假设都是可用的。我们的结果为使用数据驱动的权重进行多重测试提供了一个新的视角:虽然标准加权多重测试方法要求权重确定性地与被测试的假设数量相加，但我们表明，当权重是独立于p值的e值时，不需要这种归一化。这样的e值可以在meta分析中获得，其中使用主数据集计算p值，使用独立的辅助数据集计算e值。在meta分析之外，我们展示了可以在单个数据集本身上构建独立e值和p值的设置。我们的程序可以导致功率的大幅增加，特别是如果非零假设的e值远大于1。

引用次数: 14

Retrospective causal inference with multiple effect variables 多效应变量的回顾性因果推理

2区数学 Q2 BIOLOGY

Biometrika

Pub Date : 2023-09-14 DOI: 10.1093/biomet/asad056

Wei Li, Zitong Lu, Jinzhu Jia, Min Xie, Zhi Geng

Summary As highlighted in Dawid (2000) and Pearl & Mackenzie (2018), deducing the causes of given effects is a more challenging problem than evaluating the effects of causes in causal inference. Lu et al. (2023) proposed an approach for deducing causes of a single effect variable based on posterior causal effects. In many applications, there are multiple effect variables, and thus they can be used simultaneously to more accurately deduce the causes. To retrospectively deduce causes from multiple effects, we propose multivariate posterior total, intervention and direct causal effects conditional on the observed evidence. We describe the assumptions of no-confounding and monotonicity, under which we prove identifiability of the multivariate posterior causal effects and provide their identification equations. The proposed approach can be applied for causal attributions, medical diagnosis, blame and responsibility in various studies with multiple effect or outcome variables. Two examples are used to illustrate the proposed approach.

david(2000)和Pearl &Mackenzie(2018)认为，在因果推理中，推断给定结果的原因比评估原因的影响更具挑战性。Lu等人(2023)提出了一种基于后验因果效应的方法来推断单个效应变量的原因。在许多应用中，有多个影响变量，因此可以同时使用它们来更准确地推断原因。为了从多重影响中回顾性地推断原因，我们提出了基于观察证据的多元后验效应、干预效应和直接因果效应。在无混杂和单调的假设下，我们证明了多元后验因果效应的可辨识性，并给出了它们的辨识方程。所提出的方法可以应用于各种具有多效果或结果变量的研究中的因果归因、医学诊断、责备和责任。用两个例子来说明所提出的方法。

引用次数: 0

Estimation of prediction error in time series 时间序列预测误差的估计

2区数学 Q2 BIOLOGY

Biometrika

Pub Date : 2023-09-09 DOI: 10.1093/biomet/asad053

Alexander Aue, Prabir Burman

Summary The accurate estimation of prediction errors in time series is an important problem, which has immediate implications for the accuracy of prediction intervals as well as the quality of a number of widely used time series model selection criteria such as the Akaike information criterion. Except for simple cases, however, it is difficult or even impossible to obtain exact analytical expressions for one-step and multi-step predictions. This may be one of the reasons that, unlike in the independent case (see Efron, 2004), up to now there has been no fully established methodology for time series prediction error estimation. Starting from an approximation to the bias-variance decomposition of the squared prediction error, a method for accurate estimation of prediction errors in both univariate and multivariate stationary time series is developed in this article. In particular, several estimates are derived for a general class of predictors that includes most of the popular linear, nonlinear, parametric and nonparametric time series models used in practice, with causal invertible autoregressive moving average and nonparametric autoregressive processes discussed as lead examples. Simulations demonstrate that the proposed estimators perform quite well in finite samples. The estimates may also be used for model selection when the purpose of modelling is prediction.

时间序列预测误差的准确估计是一个重要的问题，它直接关系到预测区间的准确性以及一些广泛使用的时间序列模型选择准则(如赤池信息准则)的质量。然而，除了简单的情况外，很难甚至不可能获得一步和多步预测的精确解析表达式。这可能是原因之一，不像在独立的情况下(见Efron, 2004)，到目前为止，还没有完全建立的方法来估计时间序列预测误差。本文从对预测误差平方的偏方差分解的近似出发，提出了一种单变量和多变量平稳时间序列预测误差的精确估计方法。特别是，对一般类型的预测器进行了一些估计，其中包括大多数流行的线性，非线性，参数和非参数时间序列模型，在实践中使用，因果可逆自回归移动平均和非参数自回归过程作为主要例子讨论。仿真结果表明，所提出的估计器在有限样本下具有良好的性能。当建模的目的是预测时，估计也可用于模型选择。

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引用次数: 0

More Efficient Exact Group Invariance Testing: using a Representative Subgroup 更有效的精确群不变性测试：使用代表子群

IF 2.7 2区数学 Q2 BIOLOGY

Biometrika

Pub Date : 2023-09-01 DOI: 10.1093/biomet/asad050

N. W. Koning, J. Hemerik

We consider testing invariance of a distribution under an algebraic group of transformations, such as permutations or sign-flips. As such groups are typically huge, tests based on the full group are often computationally infeasible. Hence, it is standard practice to use a random subset of transformations. We improve upon this by replacing the random subset with a strategically chosen, fixed subgroup of transformations. In a generalized location model, we show that the resulting tests are often consistent for lower signal-to-noise ratios. Moreover, we establish an analogy between the power improvement and switching from a t-test to a Z-test under normality. Importantly, in permutation-based multiple testing, the efficiency gain with our approach can be huge, since we attain the same power with much fewer permutations.

我们考虑在置换或符号翻转等变换的代数群下检验分布的不变性。由于这样的组通常是巨大的，基于整个组的测试通常在计算上是不可行的。因此，使用转换的随机子集是标准实践。我们通过用策略选择的固定变换子群替换随机子集来改进这一点。在广义的位置模型中，我们表明，在较低的信噪比下，结果测试通常是一致的。此外，我们建立了功率改进与正态性下从t检验切换到z检验之间的类比。重要的是，在基于排列的多重测试中，使用我们的方法可以获得巨大的效率增益，因为我们可以用更少的排列获得相同的功率。

引用次数: 0

Marginal proportional hazards models for multivariate interval-censored data. 多变量区间删失数据的边际比例危害模型。

IF 2.4 2区数学 Q2 BIOLOGY

Biometrika

Pub Date : 2023-09-01 Epub Date: 2022-11-02 DOI: 10.1093/biomet/asac059

Yangjianchen Xu, Donglin Zeng, D Y Lin

Multivariate interval-censored data arise when there are multiple types of events or clusters of study subjects, such that the event times are potentially correlated and when each event is only known to occur over a particular time interval. We formulate the effects of potentially time-varying covariates on the multivariate event times through marginal proportional hazards models while leaving the dependence structures of the related event times unspecified. We construct the nonparametric pseudolikelihood under the working assumption that all event times are independent, and we provide a simple and stable EM-type algorithm. The resulting nonparametric maximum pseudolikelihood estimators for the regression parameters are shown to be consistent and asymptotically normal, with a limiting covariance matrix that can be consistently estimated by a sandwich estimator under arbitrary dependence structures for the related event times. We evaluate the performance of the proposed methods through extensive simulation studies and present an application to data from the Atherosclerosis Risk in Communities Study.

当存在多种类型的事件或研究对象集群时，就会产生多变量区间删失数据，从而使事件时间具有潜在的相关性，并且每个事件只在特定的时间区间内发生。我们通过边际比例危险模型来计算可能随时间变化的协变量对多元事件时间的影响，同时不指定相关事件时间的依赖结构。我们在所有事件时间都是独立的工作假设下构建了非参数伪概率，并提供了一种简单稳定的 EM 型算法。结果表明，回归参数的非参数最大伪似然估计值是一致的、渐近正态的，其极限协方差矩阵可以在相关事件时间的任意依赖结构下通过三明治估计值进行一致估计。我们通过大量的模拟研究评估了所提方法的性能，并介绍了对社区动脉粥样硬化风险研究数据的应用。

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引用次数: 0

ASSESSING TIME-VARYING CAUSAL EFFECT MODERATION IN THE PRESENCE OF CLUSTER-LEVEL TREATMENT EFFECT HETEROGENEITY AND INTERFERENCE. 在集群水平治疗效果异质性和干扰存在的情况下评估时变因果效应调节。

IF 2.7 2区数学 Q2 BIOLOGY

Biometrika

Pub Date : 2023-09-01 DOI: 10.1093/biomet/asac065

Jieru Shi, Zhenke Wu, Walter Dempsey

The micro-randomized trial (MRT) is a sequential randomized experimental design to empirically evaluate the effectiveness of mobile health (mHealth) intervention components that may be delivered at hundreds or thousands of decision points. MRTs have motivated a new class of causal estimands, termed "causal excursion effects", for which semiparametric inference can be conducted via a weighted, centered least squares criterion (Boruvka et al., 2018). Existing methods assume between-subject independence and non-interference. Deviations from these assumptions often occur. In this paper, causal excursion effects are revisited under potential cluster-level treatment effect heterogeneity and interference, where the treatment effect of interest may depend on cluster-level moderators. Utility of the proposed methods is shown by analyzing data from a multi-institution cohort of first year medical residents in the United States.

微随机试验(MRT)是一种顺序随机实验设计，旨在经验性地评估可能在数百或数千个决策点提供的移动医疗(mHealth)干预组件的有效性。mrt激发了一类新的因果估计，称为“因果偏移效应”，其中半参数推理可以通过加权的中心最小二乘准则进行(Boruvka等人，2018)。现有的方法假设主体间独立性和不干涉性。偏离这些假设的情况经常发生。本文在潜在的集群水平治疗效应异质性和干扰下重新审视了因果偏移效应，其中感兴趣的治疗效应可能取决于集群水平调节因子。通过分析来自美国多机构的第一年住院医生队列的数据，显示了所提出方法的效用。

引用次数: 2

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