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多元正态均值的精确置信集AI 解读

A class of confidence sets with constant coverage probability for the mean of a p-variate normal distribution is proposed through a pseudo-empirical-Bayes construction. When the dimension is greater than 2, by combining analytical results with some exact numerical calculations the proposed sets are proved to have a uniformly smaller volume than the usual confidence region. Sufficient conditions for the connectedness of the proposed confidence sets are also derived. In…

利用后验协方差矩阵研究随机回归的强一致性AI 解读

In this paper we use posterior covariance matrices to study the strong consistency of Bayes estimators in stochastic regression models under various assumptions on the stochastic regressors. The random errors are assumed to form a martingale difference sequence. Several results are obtained using a recursion satisfied by the sequence of posterior covariance matrices. These results suggest that the posterior covariance matrix is a useful tool in studying strong consistency…

利用非参数先验合并多个实验的信息AI 解读

This paper considers combining information from several experiments when the experiments can be summarised via a parameter value. The structure of this set of parameters, in terms of independence, exchangeability, partial exchangeability, etc., is assumed to be unknown and a finite number of possible structures are entertained, each with an associated prior weight representing the degree of belief in that structure. Crucial is the criterion by which these structures are…

非高斯观测时间序列的似然分析AI 解读

In this paper we provide methods for estimating non-Gaussian time series models. These techniques rely on Markov chain Monte Carlo to carry out simulation smoothing and Bayesian posterior analysis of parameters, and on importance sampling to estimate the likelihood function for classical inference. The time series structure of the models is used to ensure that our simulation algorithms are efficient.

含协变量测量误差的病例对照研究贝叶斯半参数模型AI 解读

We develop a model and a numerical estimation scheme for a Bayesian approach to inference in case-control studies with errors in covariables. The model proposed in this paper is based on a nonparametric model for the unknown joint distribution for the missing data, the observed covariates and the proxy. This nonparametric distribution defines the measurement error component of the model which relates the missing covariates X with a proxy W. The oxymoron ‘nonparametric Bayes’…

非负贝叶斯时间序列模型的性质与推广AI 解读

Summary We study the most basic Bayesian forecasting model for exponential family time series, the power steady model (PSM) of Smith, in terms of observable properties of one-step forecast distributions and sample paths. The PSM implies a constraint between location and spread of the forecast distribution. Including a scale parameter in the models does not always give an exact solution free of this problem, but it does suggest how to define related models free of the…

生存数据的半参数贝叶斯分析AI 解读

This review article investigates the potential of Bayes methods for the analysis of survival data using semiparametric models based on either the hazard or the intensity function. The nonparametric part of every model is assumed to be a realization of a stochastic process. The parametric part, which may include a regression parameter or a parameter quantifying the heterogeneity of a population, is assumed to have a prior distribution with possibly unknown hyperparameters.…

共同协方差矩阵下两个多元正态总体的贝叶斯判别AI 解读

Here Bayesian and classical estimates of P, the probability that a new observation belongs to one of two multivariate normal populations with equal covariance matrices, are compared. In particular, the regions of location of a new observation for which the estimates differ are shown. The Bayesian and classical allocation rule contours are given and their differences highlighted. The posterior moments of L, the log-density ratio for a new observation, are given, and the…

层级选择模型及其在元分析中的应用AI 解读

Hierarchical selection models are introduced and shown to be useful in meta-analysis. These models combine the use of hierarchical models, allowing investigation of variability both within and between studies, and weight functions, allowing modeling of nonrandomly selected studies. Markov chain Monte Carlo (MCMC) methods are used to estimate the hierarchical selection model. This is first illustrated for known weight functions, and then extended to allow for estimation of…

利用正态混合模型进行实用贝叶斯密度估计AI 解读

Mixtures of normals provide a flexible model for estimating densities in a Bayesian framework. There are some difficulties with this model, however. First, standard reference priors yield improper posteriors. Second, the posterior for the number of components in the mixture is not well defined (if the reference prior is used). Third, posterior simulation does not provide a direct estimate of the posterior for the number of components. We present some practical methods for…

结合模拟与渐近近似计算贝叶斯因子AI 解读

The Bayes factor is a ratio of two posterior normalizing constants, which may be difficult to compute. We compare several methods of estimating Bayes factors when it is possible to simulate observations from the posterior distributions, via Markov chain Monte Carlo or other techniques. The methods that we study are all easily applied without consideration of special features of the problem, provided that each posterior distribution is well behaved in the sense of having a…

全国健康访谈调查中二元变量的小区域推断AI 解读

The National Health Interview Survey is designed to produce precise estimates of finite population parameters for the entire United States but not for small geographical areas or subpopulations. Our investigation concerns estimates of proportions such as the probability of at least one visit to a doctor within the past 12 months. To include all sources of variation in the model, we carry out a Bayesian hierarchical analysis for the desired finite population quantities.…

医疗服务提供者绩效画像的统计方法与应用AI 解读

Recent public debate on costs and effectiveness of health care in the United States has generated a growing emphasis on “profiling” of medical care providers. The process of profiling involves comparing resource use and quality of care among medical providers to a community or a normative standard. This is valuable for targeting quality improvement strategies. For example, hospital profiles may be used to determine whether institutions deviate in important ways in the…

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虚拟贝叶斯实施AI 解读

Allowing for incomplete information, this paper characterizes the social choice functions that can be approximated by the equilibrium outcomes of a mechanism: incentive compatibility is necessary and almost sufficient for virtual Bayesian implementability. In conjunction with a second condition, Bayesian incentive consistency, incentive compatibility is also sufficient. This new condition is weak--under standard topological and informational assumptions it is satisfied by…

删失数据的一类加权自助法研究AI 解读

Edgeworth expansions are derived for a class of weighted bootstrap methods for the Kaplan-Meier and Nelson-Aalen estimates using the methods contained in the monograph by Barbe and Bertail. Von Mises representations up to the third order are established for the weighted bootstrap versions of these estimators. It is shown that there exists weights which outperform Efron's bootstrap method in terms of coverage accuracy. Moreover, it is shown that this holds for a particular…

估计归一化常数比值的蒙特卡洛方法AI 解读

Recently, estimating ratios of normalizing constants has played an important role in Bayesian computations. Applications of estimating ratios of normalizing constants arise in many aspects of Bayesian statistical inference. In this article, we present an overview and discuss the current Monte Carlo methods for estimating ratios of normalizing constants. Then we propose a new ratio importance sampling method and establish its theoretical framework. We find that the ratio…

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设计性缺失数据下的贝叶斯多变量空间插值AI 解读

Summary In a network of s g sites, responses like levels of airborne pollutant concentrations may be monitored over time. The sites need not all measure the same set of response items and unmeasured items are considered as data missing by design. We propose a hierarchical Bayesian approach to interpolate the levels of, say, k responses at s u other locations called ungauged sites and also the unmeasured levels of the k responses at the gauged sites. Our method involves two…

可忽略性、充分性与辅助性AI 解读

Summary This paper explores the relationship between ignorability, sufficiency and ancillarity in the coarse data model of Heitjan and Rubin. Bayes or likelihood ignorability has a natural relationship to sufficiency, and frequentist ignorability an analogous relationship to ancillarity. Weaker conditions, termed observed likelihood sufficiency, observed specific sufficiency and observed ancillarity, expand the concepts to models where the coarsening mechanism is sometimes,…

Gibbs 采样器的更新方案、相关结构、分块与参数化AI 解读

Summary In this paper many convergence issues concerning the implementation of the Gibbs sampler are investigated. Exact computable rates of convergence for Gaussian target distributions are obtained. Different random and non-random updating strategies and blocking combinations are compared using the rates. The effect of dimensionality and correlation structure on the convergence rates are studied. Some examples are considered to demonstrate the results. For a Gaussian image…

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最后通牒议价分析：形状约束下两条效力曲线的贝叶斯比较AI 解读

An experiment designed to test whether experimenter observation influences play of the ultimatum game led to a comparison of proportions of perfect equilibria obtained under different conditions. The authors' analysis features a Bayesian approach to this comparison. Their method extends recent work in the nonparametric Bayesian analysis of bioassay problems when the prior constrains the form of the potency curve. Sampling-based approaches to calculating posterior features of…

自回归时间序列面板数据的贝叶斯分析AI 解读

The authors describe a Bayesian hierarchical model to analyze autoregressive time series panel data. They develop two algorithms using Markov-chain Monte Carlo methods, a restricted algorithm that enforces stationarity or nonstationarity conditions on the series, and an unrestricted algorithm that does not. Two examples show that restricting stationary series to be stationary provides no new information but restricting nonstationary series to be stationary leads to…