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Hamiltonian／混合蒙特卡洛中的动能选择AI 解读

We consider how different choices of kinetic energy in Hamiltonian Monte Carlo affect algorithm performance. To this end, we introduce two quantities which can be easily evaluated, the composite gradient and the implicit noise. Results are established on integrator stability and geometric convergence, and we show that choices of kinetic energy that result in heavy-tailed momentum distributions can exhibit an undesirable negligible moves property, which we define. A general…

差异马尔可夫随机场分析及微生物群落网络差异检测AI 解读

Micro-organisms such as bacteria form complex ecological community networks that can be greatly influenced by diet and other environmental factors. Differential analysis of microbial community structures aims to elucidate systematic changes during an adaptive response to changes in environment. In this paper, we propose a flexible Markov random field model for microbial network structure and introduce a hypothesis testing framework for detecting differences between networks,…

回归残差过程的自助法：是否需要平滑？AI 解读

In this paper we consider a location model of the form $Y = m(X) + \varepsilon$, where $m(\cdot)$ is the unknown regression function, the error $\varepsilon$ is independent of the $p$-dimensional covariate $X$ and $E(\varepsilon)=0$. Given i.i.d. data $(X_1,Y_1),\ldots,(X_n,Y_n)$ and given an estimator $\hat m(\cdot)$ of the function $m(\cdot)$ (which can be parametric or nonparametric of nature), we estimate the distribution of the error term $\varepsilon$ by the empirical…

降采样与混频时间序列中结构向量自回归模型的可识别性与估计AI 解读

Summary Causal inference in multivariate time series is challenging because the sampling rate may not be as fast as the time scale of the causal interactions, so the observed series is a subsampled version of the desired series. Furthermore, series may be observed at different sampling rates, yielding mixed-frequency series. To determine instantaneous and lagged effects between series at the causal scale, we take a model-based approach that relies on structural vector…

多个随机密度的 Wasserstein 协方差AI 解读

A common feature of methods for analysing samples of probability density functions is that they respect the geometry inherent to the space of densities. Once a metric is specified for this space, the Fréchet mean is typically used to quantify and visualize the average density of the sample. For one-dimensional densities, the Wasserstein metric is popular due to its theoretical appeal and interpretive value as an optimal transport metric, leading to the Wasserstein–Fréchet…

通过周期嵌入估计随机场的谱密度AI 解读

We introduce methods for estimating the spectral density of a random field on a $d$-dimensional lattice from incomplete gridded data. Data are iteratively imputed onto an expanded lattice according to a model with a periodic covariance function. The imputations are convenient computationally, in that circulant embedding and preconditioned conjugate gradient methods can produce imputations in $O(n\log n)$ time and $O(n)$ memory. However, these so-called periodic imputations…

马尔可夫链蒙特卡洛的多变量输出分析AI 解读

Markov chain Monte Carlo produces a correlated sample which may be used for estimating expectations with respect to a target distribution. A fundamental question is: when should sampling stop so that we have good estimates of the desired quantities? The key to answering this question lies in assessing the Monte Carlo error through a multivariate Markov chain central limit theorem. The multivariate nature of this Monte Carlo error has been largely ignored in the literature.…

插补调查数据的伪总体自助法AI 解读

The most common way to treat item nonresponse in surveys is to replace a missing value by a plausible value constructed on the basis of fully observed variables. Treating the imputed values as if they were observed may lead to invalid inferences. Bootstrap variance estimators for various finite population parameters are obtained using two pseudo-population bootstrap schemes. We establish the asymptotic properties of the resulting bootstrap variance estimators for population…

一般贝叶斯更新与损失似然自助法AI 解读

In this paper we revisit the weighted likelihood bootstrap, a method that generates samples from an approximate Bayesian posterior of a parametric model. We show that the same method can be derived, without approximation, under a Bayesian nonparametric model with the parameter of interest defined through minimizing an expected negative loglikelihood under an unknown sampling distribution. This interpretation enables us to extend the weighted likelihood bootstrap to posterior…

通过耦合实现无偏 Hamiltonian Monte CarloAI 解读

Summary We propose a method for parallelization of Hamiltonian Monte Carlo estimators. Our approach involves constructing a pair of Hamiltonian Monte Carlo chains that are coupled in such a way that they meet exactly after some random number of iterations. These chains can then be combined so that the resulting estimators are unbiased. This allows us to produce independent replicates in parallel and average them to obtain estimators that are consistent in the limit of the…

去偏 Whittle 似然AI 解读

The Whittle likelihood is a widely used and computationally efficient pseudolikelihood. However, it is known to produce biased parameter estimates with finite sample sizes for large classes of models. We propose a method for debiasing Whittle estimates for second-order stationary stochastic processes. The debiased Whittle likelihood can be computed in the same |${O}(n\log n)$| operations as the standard Whittle approach. We demonstrate the superior performance of our method…

干扰下因果效应的随机化检验AI 解读

Many causal questions involve interactions between units, also known as interference, for example between individuals in households, students in schools, or firms in markets. In this paper we formalize the concept of a conditioning mechanism, which provides a framework for constructing valid and powerful randomization tests under general forms of interference. We describe our framework in the context of two-stage randomized designs and apply our approach to a randomized…

一般散度损失下的层级贝叶斯与经验贝叶斯预测密度AI 解读

Consider the problem of finding a predictive density of a new observation drawn independently of observations sampled from a multivariate normal distribution with the same unknown mean vector and the same known variance under general divergence loss. In this paper, we consider two kinds of prior distribution for the mean vector: one is a multivariate normal distribution with mean based on unknown regression coefficients, and the other further assumes that the regression…

一般后验可信区域的校准AI 解读

Summary Calibration of credible regions derived from under- or misspecified models is an important and challenging problem. In this paper, we introduce a scalar tuning parameter that controls the posterior distribution spread, and develop a Monte Carlo algorithm that sets this parameter so that the corresponding credible region achieves the nominal frequentist coverage probability.

《利用隐马尔可夫模型 knockoff 寻找基因》作者回复AI 解读

We are very grateful to the editors for the opportunity to expand and deepen the reflection on the possible advantages of a knockoff approach to genome-wide association studies. The discussants bring up a number of important points, related to either the knockoffs methodology in general or its specific application to genetic studies. In this rejoinder we offer some clarifications, mention relevant recent developments, and highlight a few remaining open problems. The model-X…

有向无环图上控制错误发现率的序贯算法AI 解读

We propose a linear-time, single-pass, top-down algorithm for multiple testing on directed acyclic graphs, where nodes represent hypotheses and edges specify a partial ordering in which the hypotheses must be tested. The procedure is guaranteed to reject a sub-directed acyclic graph with bounded false discovery rate while satisfying the logical constraint that a rejected node’s parents must also be rejected. It is designed for sequential testing settings where the directed…

密度比模型下优势指数的半参数推断AI 解读

An important and often discussed research problem in statistics is how to compare several populations; examples arise in medical science, engineering, finance and other fields. Often population means or medians are compared. However, one population may have a higher mean income, for example, because of a small number of super-rich individuals; the mean therefore may not reflect the wealth of the general population. Instead, an index of the degree of stochastic dominance of…

捕获异质性下的低风险总体规模估计AI 解读

Population estimation methods are used for estimating the size of a population from samples of individuals. In many applications, the probability of being observed in the sample varies across individuals, resulting in sampling bias. We show that in this setting, estimators of the population size have high and sometimes infinite risk, leading to large uncertainty in the population size. As an alternative, we propose estimating the population of individuals with observation…

信号加噪声矩阵模型：特征向量的偏差与波动AI 解读

Estimating eigenvectors and low-dimensional subspaces is of central importance for numerous problems in statistics, computer science and applied mathematics. In this paper we characterize the behaviour of perturbed eigenvectors for a range of signal-plus-noise matrix models encountered in statistical and random-matrix-theoretic settings. We establish both first-order approximation results, i.e., sharp deviations, and second-order distributional limit theory, i.e.,…

基于计数过程的删失结局降维方法AI 解读

SUMMARY We propose counting process-based dimension reduction methods for right-censored survival data. Semiparametric estimating equations are constructed to estimate the dimension reduction subspace for the failure time model. Our methods address two limitations of existing approaches. First, using the counting process formulation, they do not require estimation of the censoring distribution to compensate for the bias in estimating the dimension reduction subspace. Second,…

任意分布下的相互独立性检验AI 解读

Statistics are proposed for testing the hypothesis that arbitrary random variables are mutually independent. The tests are consistent and well behaved for any marginal distributions; they can be used, for example, for contingency tables which are sparse or whose dimension depends on the sample size, as well as for mixed data. No regularity conditions, data jittering, or binning mechanisms are required. The statistics are rank-based functionals of Cramér–von Mises type whose…

混合治愈模型中治愈率的拟合优度检验AI 解读

We consider models for time-to-event data that allow that an event, e.g., a relapse of a disease, never occurs for a certain percentage |$p$| of the population, called the cure rate. We suppose that these data are subject to random right censoring and we model the data using a mixture cure model, in which the survival function of the uncured subjects is left unspecified. The aim is to test whether the cure rate |$p$|⁠, as a function of the covariates, satisfies a certain…

从函数数据片段恢复协方差AI 解读

We consider nonparametric estimation of a covariance function on the unit square, given a sample of discretely observed fragments of functional data. When each sample path is observed only on a subinterval of length |$\delta<1$|⁠, one has no statistical information on the unknown covariance outside a |$\delta$|-band around the diagonal. The problem seems unidentifiable without parametric assumptions, but we show that nonparametric estimation is feasible under suitable…

通过凸层级惩罚实现自适应截断的非参数回归AI 解读

SUMMARY We consider the problem of nonparametric regression with a potentially large number of covariates. We propose a convex, penalized estimation framework that is particularly well suited to high-dimensional sparse additive models and combines the appealing features of finite basis representation and smoothing penalties. In the case of additive models, a finite basis representation provides a parsimonious representation for fitted functions but is not adaptive when…