EMPIRICAL BAYES TEST PROBLEMS OF VARIANCE COMPONENTS IN RANDOM EFFECTS MODEL

Bayes decision rule of variance components for one-way random effects model is derived and empirical Bayes (EB) decision rules are constructed by kernel estimation method. Under suitable conditions, it is shown that the proposed EB decision rules are asymptotically optimal with convergence rates near O(n^-1/2). Finally, an example concerning the main result is given.     

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??The Bayes estimators of variance components are derived under weighted square loss function for the balanced one-way classification random effects model with the assumption that variance component has the conjugate prior distribution. The superiorities of the Bayes estimators for variance components to traditional ANOVA estimators are studied in terms of the mean square error (MSE) criterion. Finally, a remark for main results is given.     

随机效应模型中方差分量渐近最优的经验Bayes估计

本文在加权二次损失下导出了双向分类随机效应模型中方差分量的Bayes估计,并利用多元密度函数及其混合偏导数核估计的方法构造了方差分量的经验Bayes(EB)估计.在适当的条件下证明了EB估计的渐近最优性,给出了模型的特例和推广.最后,举出一个满足定理条件的例子.     

单向分类随机效应模型中方差分量的渐近最优经验Bayes估计

本文在加权平方损失下导出了单向分类随机效应模型中方差分量的Bayes估计, 利用多元密度及其偏导数的核估计方法构造了方差分量的经验Bayes(EB)估计,证明了 EB估计的渐近最优性.文末还给出了一个例子说明了符合定理条件的先验分布是存在 的.     

随机效应模型中方差分量的经验Bayes检验问题

给出了双向分类随机效应模型中方差分量的Bayes检验的判决函数,利用核估计的方法,构造了相应的经验Bayes(EB)检验的判决函数．在适当的条件下证明了EB判决函数是渐近最优的且有收敛速度．给出了模型的特例和推广．最后,举出一个满足定理条件的例子．     

非平衡随机效应模型中方差分量的经验Bayes估计

对非平衡单向分类随机效应模型中方差分量找到了其最小充分统计量,在加权平方损失下导出了其Bayes估计,利用多元密度及其偏导数的核估计方法构造了方差分量的经验Bayes(EB)估计,并导出了其收敛速度.文末用例子说明了符合定理条件的先验分布是存在的.     

Honest Importance Sampling With Multiple Markov Chains

Importance sampling is a classical Monte Carlo technique in which a random sample from one probability density, π₁, is used to estimate an expectation with respect to another, π. The importance sampling estimator is strongly consistent and, as long as two simple moment conditions are satisfied, it obeys a central limit theorem (CLT). Moreover, there is a simple consistent estimator for the asymptotic variance in the CLT, which makes for routine computation of standard errors. Importance sampling can also be used in the Markov chain Monte Carlo (MCMC) context. Indeed, if the random sample from π₁ is replaced by a Harris ergodic Markov chain with invariant density π₁, then the resulting estimator remains strongly consistent. There is a price to be paid, however, as the computation of standard errors becomes more complicated. First, the two simple moment conditions that guarantee a CLT in the iid case are not enough in the MCMC context. Second, even when a CLT does hold, the asymptotic variance has a complex form and is difficult to estimate consistently. In this article, we explain how to use regenerative simulation to overcome these problems. Actually, we consider a more general setup, where we assume that Markov chain samples from several probability densities, π₁, …, π_k, are available. We construct multiple-chain importance sampling estimators for which we obtain a CLT based on regeneration. We show that if the Markov chains converge to their respective target distributions at a geometric rate, then under moment conditions similar to those required in the iid case, the MCMC-based importance sampling estimator obeys a CLT. Furthermore, because the CLT is based on a regenerative process, there is a simple consistent estimator of the asymptotic variance. We illustrate the method with two applications in Bayesian sensitivity analysis. The first concerns one-way random effect models under different priors. The second involves Bayesian variable selection in linear regression, and for this application, importance sampling based on multiple chains enables an empirical Bayes approach to variable selection.     

有偏抽样下带信息观察和删失的面板数据的统计分析

面板数据经常出现在许多研究领域, 比如纵向跟踪研究. 在很多情况下, 纵向反应变量与观察 时间和删失时间都有关系. 本文在有偏抽样下, 针对这些相关性存在的情况, 利用一个不能观察的潜在 变量, 提出了一个联合建模方法来刻画纵向反应变量与观察时间和删失时间的相关性, 获得了模型中 回归参数的估计方程以及估计的渐近性质, 并通过数值模拟验证了这些估计在小样本下也是有效的, 同时把该估计方法用于一组实际的膀胱癌数据分析中.     

Two-component Poisson mixture regression modelling of count data with bivariate random effects

Two-component Poisson mixture regression is typically used to model heterogeneous count outcomes that arise from two underlying sub-populations. Furthermore, a random component can be incorporated into the linear predictor to account for the clustering data structure. However, when including random effects in both components of the mixture model, the two random effects are often assumed to be independent for simplicity. A two-component Poisson mixture regression model with bivariate random effects is proposed to deal with the correlated situation. A restricted maximum quasi-likelihood estimation procedure is provided to obtain the parameter estimates of the model. A simulation study shows both fixed effects and variance component estimates perform well under different conditions. An application to childhood gastroenteritis data demonstrates the usefulness of the proposed methodology, and suggests that neglecting the inherent correlation between random effects may lead to incorrect inferences concerning the count outcomes.     

你也需要蒙特卡罗方法——提高应用水平的若干技巧

本文是《你也需要蒙特卡罗方法》中的第二篇。文中讨论提高应用水平的一些技巧,涉及模拟模型的选取,提高计算速度或降低抽样方差的一些方法,诸如重要抽样、相关抽样、对偶抽样和分层抽样等。还讨论了模拟中所需的抽样次数的确定和模拟结果的精度评估等实用问题。     

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本文利用广义p-值和广义置信区间的概念构造 含有三个随机效应的套误差分量模型中方差分量的几种新的精确检验和置信区间, 并讨论它们在尺度变换下的不变性. 模拟结果表明, 基于广义p-值的检验很好地控制了犯第一类错误的概率.     

Bayesian analysis of non-linear structural equation models with non-ignorable missing outcomes from reproductive dispersion models

Non-linear structural equation models are widely used to analyze the relationships among outcomes and latent variables in modern educational, medical, social and psychological studies. However, the existing theories and methods for analyzing non-linear structural equation models focus on the assumptions of outcomes from an exponential family, and hence can’t be used to analyze non-exponential family outcomes. In this paper, a Bayesian method is developed to analyze non-linear structural equation models in which the manifest variables are from a reproductive dispersion model (RDM) and/or may be missing with non-ignorable missingness mechanism. The non-ignorable missingness mechanism is specified by a logistic regression model. A hybrid algorithm combining the Gibbs sampler and the Metropolis–Hastings algorithm is used to obtain the joint Bayesian estimates of structural parameters, latent variables and parameters in the logistic regression model, and a procedure calculating the Bayes factor for model comparison is given via path sampling. A goodness-of-fit statistic is proposed to assess the plausibility of the posited model. A simulation study and a real example are presented to illustrate the newly developed Bayesian methodologies.     

随机截尾试验变量抽样接收方案的贝叶斯决策

本运用Bayes决策理论研究指数分布和随机截尾试验的抽样接收方案的一般模型,我们证明了最优Bayes法则具有单调性,并对二个特殊的决策损失函数给出了最优Bayes法则和Bayes风险的具体表达式。     

Semiparametric analysis of longitudinal data with informative observation times

In many longitudinal studies,observation times as well as censoring times may be correlated with longitudinal responses.This paper considers a multiplicative random effects model for the longitudinal response where these correlations may exist and a joint modeling approach is proposed via a shared latent variable.For inference about regression parameters,estimating equation approaches are developed and asymptotic properties of the proposed estimators are established.The finite sample behavior of the methods is examined through simulation studies and an application to a data set from a bladder cancer study is provided for illustration.     

Optimal subsampling for large-scale quantile regression

To deal with massive data sets, subsampling is known as an effective method which can significantly reduce computational costs in estimating model parameters. In this article, an efficient subsampling method is developed for large-scale quantile regression via Poisson sampling framework, which can solve the memory constraint problem imposed by big data. Under some mild conditions, large sample properties for the estimator involving the weak and strong consistencies, and asymptotic normality are established. Furthermore, the optimal subsampling probabilities are derived according to the A-optimality criterion. It is shown that the estimator based on the optimal subsampling asymptotically achieves a smaller variance than that by the uniform random subsampling. The proposed method is illustrated and evaluated through numerical analyses on both simulated and real data sets.     

Random sampling within the framework of a multivariate principal-agent approach

In this paper, we analyze a specific class of principal-agent models which seems to be sufficiently general to cover applications in environmental economics with upstream-downstream problems as an example. In our basic model, the observation outcome is ann-dimensional random vectorx and only the first and second moments ofx are common knowledge. We study the effects of random sampling in the presence of costly signals. For this purpose, we assume that the principal and the agent use a simple statistical procedure, i.e. their contract will be based on the mean of a random sample with sampling costs dependent on the sample size. It is shown that there exists an optimal sample size. We investigate the relationship between the optimal sample size, the marginal sampling costs, and the agent's risk aversion.     

Posterior propriety in nonparametric mixed effects model

It is well known that spline smoothing estimator relates to the Bayesian estimate under partially informative normal prior.In this paper,we derive the conditions for the propriety of the posterior in the nonparametric mixed efects model under this class of partially informative normal prior for fxed efect with inverse gamma priors on the variance components and hierarchical priors for covariance matrix of random efect,then we explore the Gibbs sampling procedure.     

Objective Bayesian model selection approach to the two way analysis of variance

An objective Bayesian procedure for testing in the two way analysis of variance is proposed. In the classical methodology the main effects of the two factors and the interaction effect are formulated as linear contrasts between means of normal populations, and hypotheses of the existence of such effects are tested. In this paper, for the first time these hypotheses have been formulated as objective Bayesian model selection problems. Our development is under homoscedasticity and heteroscedasticity, providing exact solutions in both cases. Bayes factors are the key tool to choose between the models under comparison but for the usual default prior distributions they are not well defined. To avoid this difficulty Bayes factors for intrinsic priors are proposed and they are applied in this setting to test the existence of the main effects and the interaction effect. The method has been illustrated with an example and compared with the classical method. For this example, both approaches went in the same direction although the large P value for interaction (0.79) only prevents us against to reject the null, and the posterior probability of the null (0.95) was conclusive.     

Bayesian model selection approach to the one way analysis of variance under homoscedasticity

An objective Bayesian model selection procedure is proposed for the one way analysis of variance under homoscedasticity. Bayes factors for the usual default prior distributions are not well defined and thus Bayes factors for intrinsic priors are used instead. The intrinsic priors depend on a training sample which is typically a unique random vector. However, for the homoscedastic ANOVA it is not the case. Nevertheless, we are able to illustrate that the Bayes factors for the intrinsic priors are not sensitive to the minimal training sample chosen; furthermore, we propose an alternative pooled prior that yields similar Bayes factors. To compute these Bayes factors Bayesian computing methods are required when the sample sizes of the involved populations are large. Finally, a one to one relationship—which we call the calibration curve—between the posterior probability of the null hypothesis and the classical $p$ value is found, thus allowing comparisons between these two measures of evidence. The behavior of the calibration curve as a function of the sample size is studied and conclusions relating both procedures are stated.     

戈德菲尔德匡特检验的推广

在大多数经济现象中,回归模型的随机扰动项并不具有同方差性,它可能随观察值的不同而变化。对这种异方差模型进行最小二乘估计,会产生严重的后果,因此研究异方差的检验方法具有重要意义。由于戈德菲尔德 匡特检验方法只适用于一个自变量,因此,本文对G Q检验进行了推广,说明在多变量的情况下,可以利用主成分对样本数据进行排序,从而解决了对多变量数据的排序问题,使戈德菲尔德 匡特异方差检验得到了推广,并举实例说明。