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贝叶斯稀疏线性回归的神经元化先验AI 解读

Although Bayesian variable selection methods have been intensively studied, their routine use in practice has not caught up with their non-Bayesian counterparts such as Lasso, likely due to difficulties in both computations and flexibilities of prior choices. To ease these challenges, we propose the neuronized priors to unify and extend some popular shrinkage priors, such as Laplace, Cauchy, horseshoe, and spike-and-slab priors. A neuronized prior can be written as the…

基于多受试者时间序列的多层偏相关推断AI 解读

Partial correlations are commonly used to analyze the conditional dependence among variables. In this work, we propose a hierarchical model to study both the subject- and population-level partial correlations based on multi-subject time-series data. Multiple testing procedures adaptive to temporally dependent data with false discovery proportion control are proposed to identify the nonzero partial correlations in both the subject and population levels. A computationally…

时变随机对象与动态网络的建模AI 解读

Samples of dynamic or time-varying networks and other random object data such as time-varying probability distributions are increasingly encountered in modern data analysis. Common methods for time-varying data such as functional data analysis are infeasible when observations are time courses of networks or other complex non-Euclidean random objects that are elements of general metric spaces. In such spaces, only pairwise distances between the data objects are available and…

高维时间序列的断点推断AI 解读

For multiple change-points detection of high-dimensional time series, we provide asymptotic theory concerning the consistency and the asymptotic distribution of the breakpoint statistics and estimated break sizes. The theory backs up a simple two-step procedure for detecting and estimating multiple change-points. The proposed two-step procedure involves the maximum of a MOSUM (moving sum) type statistics in the first step and a CUSUM (cumulative sum) refinement step on an…

有偏抽样下的独立性检验AI 解读

Testing for dependence between pairs of random variables is a fundamental problem in statistics. In some applications, data are subject to selection bias that can create spurious dependence. An important example is truncation models, in which observed pairs are restricted to a specific subset of the X-Y plane. Standard tests for independence are not suitable in such cases, and alternative tests that take the selection bias into account are required. Here, we generalize the…

分位数回归中的单指标门限模型AI 解读

Threshold regression models are useful for identifying subgroups with heterogeneous parameters. The conventional threshold regression models split the sample based on a single and observed threshold variable, which enforces the threshold point to be equal for all subgroups of the population. In this article, we consider a more flexible single-index threshold model in the quantile regression setup, in which the sample is split based on a linear combination of predictors. We…

多模态数据的整合因子回归及其推断AI 解读

Multimodal data, where different types of data are collected from the same subjects, are fast emerging in a large variety of scientific applications. Factor analysis is commonly used in integrative analysis of multimodal data, and is particularly useful to overcome the curse of high dimensionality and high correlations. However, there is little work on statistical inference for factor analysis based supervised modeling of multimodal data. In this article, we consider an…

非可微先验下贝叶斯推断的梯度型 MCMCAI 解读

The use of nondifferentiable priors in Bayesian statistics has become increasingly popular, in particular in Bayesian imaging analysis. Current state-of-the-art methods are approximate in the sense that they replace the posterior with a smooth approximation via Moreau-Yosida envelopes, and apply gradient-based discretized diffusions to sample from the resulting distribution. We characterize the error of the Moreau-Yosida approximation and propose a novel implementation using…

保护个体数据的高维异质研究整合回归AI 解读

Evidence-based decision making often relies on meta-analyzing multiple studies, which enables more precise estimation and investigation of generalizability. Integrative analysis of multiple heterogeneous studies is, however, highly challenging in the ultra high-dimensional setting. The challenge is even more pronounced when the individual-level data cannot be shared across studies, known as DataSHIELD contraint. Under sparse regression models that are assumed to be similar…

半监督线性回归AI 解读

We study a regression problem where for some part of the data we observe both the label variable (Y) and the predictors (X), while for other part of the data only the predictors are given. Such a problem arises, for example, when observations of the label variable are costly and may require a skilled human agent. When the conditional expectation E[Y|X] is not exactly linear, one can consider the best linear approximation to the conditional expectation, which can be estimated…

聚类分区随机试验的设计型比率估计与中心极限定理AI 解读

This article develops design-based ratio estimators for clustered, blocked randomized controlled trials (RCTs), with an application to a federally funded, school-based RCT testing the effects of behavioral health interventions. We consider finite population weighted least-square estimators for average treatment effects (ATEs), allowing for general weighting schemes and covariates. We consider models with block-by-treatment status interactions as well as restricted models…

可交换结构化交互过程的分层网络模型AI 解读

Network data often arises via a series of structured interactions among a population of constituent elements. E-mail exchanges, for example, have a single sender followed by potentially multiple receivers. Scientific articles, on the other hand, may have multiple subject areas and multiple authors. We introduce a statistical model, termed the Pitman-Yor hierarchical vertex components model (PY-HVCM), that is well suited for structured interaction data. The proposed PY-HVCM…

数据集偏移下的广义贝叶斯类别比例学习AI 解读

Quantification learning is the task of prevalence estimation for a test population using predictions from a classifier trained on a different population. Quantification methods assume that the sensitivities and specificities of the classifier are either perfect or transportable from the training to the test population. These assumptions are inappropriate in the presence of dataset shift, when the misclassification rates in the training population are not representative of…

多参数非参数融合学习：结合数据深度与置信分布AI 解读

Fusion learning refers to synthesizing inferences from multiple sources or studies to make a more effective inference and prediction than from any individual source or study alone. Most existing methods for synthesizing inferences rely on parametric model assumptions, such as normality, which often do not hold in practice. We propose a general nonparametric fusion learning framework for synthesizing inferences for multiparameters from different studies. The main tool…

配对随机实验中的推断AI 解读

This article studies inference for the average treatment effect in randomized controlled trials where treatment status is determined according to a “matched pairs” design. By a “matched pairs” design, we mean that units are sampled iid from the population of interest, paired according to observed, baseline covariates and finally, within each pair, one unit is selected at random for treatment. This type of design is used routinely throughout the sciences, but fundamental…

网络函数型变系数模型AI 解读

We consider functional responses with network dependence observed for each individual at irregular time points. To model both the interindividual dependence and within-individual dynamic correlation, we propose a network functional varying coefficient (NFVC) model. The response of each individual is characterized by a linear combination of responses from its connected nodes and its exogenous covariates. All the model coefficients are allowed to be time dependent. The NFVC…

高维数据变点的自适应推断AI 解读

In this article, we propose a class of test statistics for a change point in the mean of high-dimensional independent data. Our test integrates the U-statistic based approach in a recent work by Wang et al. and the Lq-norm based high-dimensional test in a recent work by He et al., and inherits several appealing features such as being tuning parameter free and asymptotic independence for test statistics corresponding to even q’s. A simple combination of test statistics…

高维响应线性模型中的线性假设检验AI 解读

In this paper, we propose a new projection test for linear hypotheses on regression coefficient matrices in linear models with high dimensional responses. We systematically study the theoretical properties of the proposed test. We first derive the optimal projection matrix for any given projection dimension to achieve the best power and provide an upper bound for the optimal dimension of projection matrix. We further provide insights into how to construct the optimal…

核常微分方程AI 解读

Ordinary differential equation (ODE) is widely used in modeling biological and physical processes in science. In this article, we propose a new reproducing kernel-based approach for estimation and inference of ODE given noisy observations. We do not assume the functional forms in ODE to be known, or restrict them to be linear or additive, and we allow pairwise interactions. We perform sparse estimation to select individual functionals, and construct confidence intervals for…

结合目标总体汇总统计与源总体个体数据的事件发生风险外推AI 解读

Predicting risks of chronic diseases has become increasingly important in clinical practice. When a prediction model is developed in a cohort, there is a great interest to apply the model to other cohorts. Due to potential discrepancy in baseline disease incidences between different cohorts and shifts in patient composition, the risk predicted by the model built in the source cohort often under- or over-estimates the risk in a new cohort. In this article, we assume the…

时间序列模型的稳健两步小波推断AI 解读

) models with additional stochastic processes are increasingly used for data analysis in biology, ecology, engineering, and economics. Inference on and/or prediction from these models can be highly challenging: (i) the data may contain outliers that can adversely affect the estimation procedure; (ii) the computational complexity can become prohibitive when the time series are extremely large; (iii) model selection adds another layer of (computational) complexity; and (iv)…

本福特定律的刻画与检验AI 解读

Benford’s law defines a probability distribution for patterns of significant digits in real numbers. When the law is expected to hold for genuine observations, deviation from it can be taken as evidence of possible data manipulation. We derive results on a transform of the significand function that provide motivation for new tests of conformance to Benford’s law exploiting its sum-invariance characterization. We also study the connection between sum invariance of the first…

嵌套误差回归模型中经验最佳线性无偏预测的渐近理论AI 解读

In this article we derive the asymptotic distribution of estimated best linear unbiased predictors (EBLUPs) of the random effects in a nested error regression model. Under very mild conditions which do not require the assumption of normality, we show that asymptotically the distribution of the EBLUPs as both the number of clusters and the cluster sizes diverge to infinity is the convolution of the true distribution of the random effects and a normal distribution. This result…

预先多重检验估计及其在多样本协方差估计中的应用AI 解读

Multisample covariance estimation—that is, estimation of the covariance matrices associated with k distinct populations—is a classical problem in multivariate statistics. A common solution is to base estimation on the outcome of a test that these covariance matrices show some given pattern. Such a preliminary test may, for example, investigate whether or not the various covariance matrices are equal to each other (test of homogeneity), or whether or not they have common…