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边际推断模型：针对目标参数的无先验概率推断AI 解读

The inferential models (IM) framework provides prior-free, frequency-calibrated, and posterior probabilistic inference. The key is the use of random sets to predict unobservable auxiliary variables connected to the observable data and unknown parameters. When nuisance parameters are present, a marginalization step can reduce the dimension of the auxiliary variable which, in turn, leads to more efficient inference. For regular problems, exact marginalization can be achieved,…

大型稀疏张量的贝叶斯分解AI 解读

It has become routine to collect data that are structured as multiway arrays (tensors). There is an enormous literature on low rank and sparse matrix factorizations, but limited consideration of extensions to the tensor case in statistics. The most common low rank tensor factorization relies on parallel factor analysis (PARAFAC), which expresses a rank k tensor as a sum of rank one tensors. When observations are only available for a tiny subset of the cells of a big tensor,…

贝叶斯压缩回归AI 解读

As an alternative to variable selection or shrinkage in high-dimensional regression, we propose to randomly compress the predictors prior to analysis. This dramatically reduces storage and computational bottlenecks, performing well when the predictors can be projected to a low-dimensional linear subspace with minimal loss of information about the response. As opposed to existing Bayesian dimensionality reduction approaches, the exact posterior distribution conditional on the…

用于最优收缩的 Dirichlet–Laplace 先验AI 解读

regularization, are routinely used in high-dimensional applications, and there is a rich literature on optimality properties under sparsity assumptions. In the Bayesian paradigm, sparsity is routinely induced through two-component mixture priors having a probability mass at zero, but such priors encounter daunting computational problems in high dimensions. This has motivated continuous shrinkage priors, which can be expressed as global-local scale mixtures of Gaussians,…

含吸收态的状态切换ARMA贝叶斯推断：事前实际利率动态AI 解读

One goal of this article is to develop an efficient Metropolis–Hastings (MH) algorithm for estimating an ARMA model with a regime-switching mean, by designing a new efficient proposal distribution for the regime-indicator variable. Unlike the existing algorithm, our algorithm can achieve reasonably fast convergence to the posterior distribution even when the latent regime-indicator variable is highly persistent or when there exist absorbing states. Another goal is to…

自适应后验集中速率AI 解读

We investigate the problem of deriving posterior concentration rates under different loss functions in nonparametric Bayes. We first provide a lower bound on posterior coverages of shrinking neighbourhoods that relates the metric or loss under which the shrinking neighbourhood is considered, and an intrinsic pre-metric linked to frequentist separation rates. In the Gaussian white noise model, we construct feasible priors based on a spike and slab procedure reminiscent of…

采用稀疏先验的贝叶斯线性回归AI 解读

We study full Bayesian procedures for high-dimensional linear regression under sparsity constraints. The prior is a mixture of point masses at zero and continuous distributions. Under compatibility conditions on the design matrix, the posterior distribution is shown to contract at the optimal rate for recovery of the unknown sparse vector, and to give optimal prediction of the response vector. It is also shown to select the correct sparse model, or at least the coefficients…

贝叶斯 T 最优模型判别设计AI 解读

The problem of constructing Bayesian optimal discriminating designs for a class of regression models with respect to the $T$-optimality criterion introduced by Atkinson and Fedorov [Biometrika 62 (1975a) 57–70] is considered. It is demonstrated that the discretization of the integral with respect to the prior distribution leads to locally $T$-optimal discriminating design problems with a large number of model comparisons. Current methodology for the numerical construction of…

存在附带参数时的模型选择AI 解读

This paper considers model selection in panels where incidental parameters are present. Primary interest centers on selecting a model that best approximates the underlying structure involving parameters that are common within the panel. It is well known that conventional model selection procedures are often inconsistent in panel models and this can be so even without nuisance parameters. Modifications are then needed to achieve consistency. New model selection information…

基于 Fisher–Rao 度量的贝叶斯敏感性分析AI 解读

We propose a geometric framework to assess sensitivity of Bayesian procedures to modelling assumptions based on the nonparametric Fisher–Rao metric. While the framework is general, the focus of this article is on assessing local and global robustness in Bayesian procedures with respect to perturbations of the likelihood and prior, and on the identification of influential observations. The approach is based on a square-root representation of densities, which enables…

利用信息矩阵近似设计含随机区组效应的广义线性模型实验AI 解读

The selection of optimal designs for generalized linear mixed models is complicated by the fact that the Fisher information matrix, on which most optimality criteria depend, is computationally expensive to evaluate. We provide two novel approximations that reduce the computational cost of evaluating the information matrix by complete enumeration of response outcomes, or Monte Carlo approximations thereof: an asymptotic approximation that is accurate when there is strong…

单调性的非参数贝叶斯检验AI 解读

This paper adopts a nonparametric Bayesian approach to testing whether a function is monotone. Two new families of tests are constructed. The first uses constrained smoothing splines with a hierarchical stochastic-process prior that explicitly controls the prior probability of monotonicity. The second uses regression splines together with two proposals for the prior over the regression coefficients. Via simulation, the finite-sample performance of the tests is shown to…

有限混合模型的阶数选择：完全似然还是观测似然信息准则？AI 解读

Choosing the number of components in a finite mixture model is a challenging task. In this article, we study the behaviour of information criteria for selecting the mixture order, based on either the observed likelihood or the complete likelihood including component labels. We propose a new observed likelihood criterion called aicmix, which is shown to be order consistent. We further show that when there is a nontrivial level of classification uncertainty in the true model,…

乘法区域模型中带基准约束的经验贝叶斯方法与风险评估AI 解读

The paper develops hierarchical empirical Bayes and benchmarked hierarchical empirical Bayes estimators of positive small area means under multiplicative models. The usual benchmarking requirement is that the small area estimates, when aggregated, should equal the direct estimates for the larger geographical areas. However, while estimating positive small area parameters, the conventional squared error or weighted squared error loss subject to the usual benchmark constraint…

贝叶斯模型不确定性中的结构马尔可夫图分布AI 解读

This paper considers the problem of defining distributions over graphical structures. We propose an extension of the hyper Markov properties of Dawid and Lauritzen [ Ann. Statist. 21 (1993) 1272–1317], which we term structural Markov properties, for both undirected decomposable and directed acyclic graphs, which requires that the structure of distinct components of the graph be conditionally independent given the existence of a separating component. This allows the analysis…

利用对数正则变动分布实现位置—尺度模型的离群值稳健性AI 解读

Estimating the location and scale parameters is common in statistics, using, for instance, the well-known sample mean and standard deviation. However, inference can be contaminated by the presence of outliers if modeling is done with light-tailed distributions such as the normal distribution. In this paper, we study robustness to outliers in location–scale parameter models using both the Bayesian and frequentist approaches. We find sufficient conditions (e.g., on tail…

摘要暂缺

《自适应非参数贝叶斯可信集的频率学覆盖》讨论AI 解读

Discussion of "Frequentist coverage of adaptive nonparametric Bayesian credible sets" by Szab\'o, van der Vaart and van Zanten [arXiv:1310.4489v5].

《自适应非参数贝叶斯可信集的频率学覆盖率》讨论AI 解读

Discussion of "Frequentist coverage of adaptive nonparametric Bayesian credible sets" by Szab\'o, van der Vaart and van Zanten [arXiv:1310.4489v5].

对《自适应非参数贝叶斯可信集的频率学覆盖率》的讨论AI 解读

VI & VIIFirst I would like to congratulate the three authors for a very nice paper.During a visit to Eindhoven in 2010, Botond Szabó and Harry van Zanten mentioned the first steps of this work to me, which concerned the understanding of certain empirical Bayes procedures in the white noise L 2 -setting.Since then, together with Aad van der Vaart, they have broadened their original goals and have produced an impressive and very interesting series of papers on the subject.The…

摘要暂缺

自适应非参数贝叶斯可信集的频率学覆盖率AI 解读

We investigate the frequentist coverage of Bayesian credible sets in a nonparametric setting. We consider a scale of priors of varying regularity and choose the regularity by an empirical Bayes method. Next we consider a central set of prescribed posterior probability in the posterior distribution of the chosen regularity. We show that such an adaptive Bayes credible set gives correct uncertainty quantification of “polished tail” parameters, in the sense of high probability…

同时纳入随机序与变异序的贝叶斯非参数 ROC 曲线估计AI 解读

Beom Seuk Hwang & Zhen ChenBeom Seuk Hwang is Postdoctoral Fellow (E-mail: ) and Zhen Chen is Investigator (E-mail: ), Biostatistics and Bioinformatics Branch, Eunice Kennedy Shriver National Institute of Child Health and Human Development, National Institutes of Health, Bethesda, MD 20892. This research was supported by the Intramural Research Program of the Eunice Kennedy Shriver National Institute of Child Health and Human Development, National Institutes of Health. This…

随研究累积追踪交叉验证预测误差估计AI 解读

In recent years, “reproducibility” has emerged as a key factor in evaluating x applications of statistics to the biomedical sciences, for example, learning predictors of disease phenotypes from high-throughput “omics” data. In particular, “validation” is undermined when error rates on newly acquired data are sharply higher than those originally reported. More precisely, when data are collected from m “studies” representing possibly different subphenotypes, more generally…