Assessing the performance of variational methods for mixed logistic regression models

We present a variational estimation method for the mixed logistic regression model. The method is based on a lower bound approximation of the logistic function [Jaakkola, J.S. and Jordan, M.I., 2000, Bayesian parameter estimation via variational methods. Statistics & Computing, 10, 25–37.]. Based on the approximation, an EM algorithm can be derived that results in a considerable simplification of the maximization problem in that it does not require the numerical evaluation of integrals over the random effects. We assess the performance of the variational method for the mixed logistic regression model in a simulation study and an empirical data example, and compare it to Laplace's method. The results indicate that the variational method is a viable choice for estimating the fixed effects of the mixed logistic regression model under the condition that the number of outcomes within each cluster is sufficiently high.     

高低分学生英语学习策略的对比研究

本研究结合问卷调查与个案访谈,比较非英语专业英语高分者和低分者的学习策略差异。研究结果表明：高分组学生对元认知策略和认知策略的使用频率显著高于低分组,而低分组学生对补偿策略的使用频率显著高于高分组;两组学生对记忆策略、情感策略和社交策略的使用频率无显著性差异,其中对社交策略两组学生均最少使用。以上结论启示我们：在英语学习中,应当注意学习策略的适当训练和合理使用,并更加重视元认知策略和社交策略的应用。     

Three-group ROC predictive analysis for ordinal outcomes

Measuring the accuracy of diagnostic tests is crucial in many application areas including medicine, machine learning, and credit scoring. The receiver operating characteristic (ROC) surface is a useful tool to assess the ability of a diagnostic test to discriminate among three-ordered classes or groups. In this article, nonparametric predictive inference (NPI) for three-group ROC analysis for ordinal outcomes is presented. NPI is a frequentist statistical method that is explicitly aimed at using few modeling assumptions, enabled through the use of lower and upper probabilities to quantify uncertainty. This article also includes results on the volumes under the ROC surfaces and consideration of the choice of decision thresholds for the diagnosis. Two examples are provided to illustrate our method.     

Bayesian prediction of order statistics with fixed and random sample sizes based on k-record values from Pareto distribution

In this paper, the two-parameter Pareto distribution is considered and the problem of prediction of order statistics from a future sample and that of its geometric mean are discussed. The Bayesian approach is applied to construct predictors based on observed k-record values for the cases when the future sample size is fixed and when it is random. Several Bayesian prediction intervals are derived. Finally, the results of a simulation study and a numerical example are presented for illustrating all the inferential procedures developed here.     

The discrepancy of P-values and posterior probability: Two-sided hypothesis of variance of normal distribution with unknown mean

This article is concerned with the comparison of P-value and Bayesian measure in point null hypothesis for the variance of Normal distribution with unknown mean. First, using fixed prior for test parameter, the posterior probability is obtained and compared with the P-value when an appropriate prior is used for the mean parameter. In the second, lower bounds of the posterior probability of H₀ under a reasonable class of prior are compared with the P-value. It has been shown that even in the presence of nuisance parameters, these two approaches can lead to different results in the statistical inference.     

Considerations on jury size and composition using lower probabilities

The use of lower probabilities is considered for inferences in basic jury scenarios to study aspects of the size of juries and their composition if society consists of subpopulations. The use of lower probability seems natural in law, as it leads to robust inference in the sense of providing a defendant with the benefit of the doubt. The method presented in this paper focusses on how representative a jury is for the whole population, using a novel concept of a second ’imaginary’ jury together with exchangeability assumptions. It has the advantage that there is an explicit absence of any assumption with regard to guilt of a defendant. Although the concept of a jury in law is central in the presentation, the novel approach and the conclusions of this paper hold for representative decision making processes in many fields, and it also provides a new perspective to stratified sampling.     

A Lower Bound for the Wrap-around L2-discrepancy on Combined Designs of Mixed Two- and Three-level Factorials

The objective of this article is to study the issue of employing the uniformity criterion measured by wrap-around L₂-discrepancy to assess the optimal foldover plans. For mixed two- and three-level fractional factorials as the original designs, general foldover plan and combined design under a foldover plan are defined, and the equivalence between any foldover plan and its complementary foldover plan is investigated. A lower bound of wrap-around L₂-discrepancy of combined designs under a general foldover plan is obtained, which can be used as a benchmark for searching optimal foldover plans. Moreover, it also provides a theoretical justification for optimal foldover plans in terms of uniformity criterion.     

Estimating population sizes by catch-effort methods

Estimating population sizes by the catch-effort methods is of enormous importance, in particular to harvest animal populations. A unified mixture model is introduced for different catchability functions to account for heterogeneous catchabilities among individual animals. A sequence of lower bounds to the odds that a single animal is not caught are proposed and used to define pseudo maximum likelihood estimators for the population size. The one-sided nature of confidence intervals is discussed. The proposed estimation methods are presented and illustrated by numerical studies.     

东营凹陷下始新统沙四段烃源岩有机相分析

目前,世界上新发现了众多深层油气藏,深层油气资源及成藏逐渐成为研究的热点。沉积有机相可以辅助对烃源岩的生烃潜力做出较好的评价,进而指导油气勘探。通过对东营凹陷下始新统沙四段烃源岩沉积特征及沉积环境、有机岩石学、有机地球化学、孢粉相等的分析,主要运用特殊元素比值、有机碳含量、镜质体发射率和孢粉相模式,将沙四段自下而上划分为盐下段的弱还原冲积扇沉积有机相、盐间段的强还原盐湖沉积有机相、盐上段的还原深湖—半深湖沉积有机相3 个有机相带。其中,以盐上段的还原深湖—半深湖沉积有机相烃源岩中保存的有机质最佳,具有良好的勘探前景,盐间段次之,盐下段较差。     

长江下游文明化进程中宗教信仰的变迁

长江下游以太湖为中心的苏皖南部与浙北地带,从新石器时代末期的良渚文化,经夏商时期点将台、湖熟、马桥文化,到周代吴、越国家社会,其文明化进程经历了繁荣——衰弱——再繁荣的曲折过程。与此相对应,长江下游的宗教信仰也经历了从史前本地传统的发达与完善、到夏商外来占卜系统的传入与发生、再到周代民间信仰的复兴与丰富的不同发展阶段。每个阶段上宗教信仰在社会生活中的地位与功能都呈现出不同特点。总体来说,长江下游文明化进程中宗教神权从与世俗王权相结合的至上地位,发展为与王权分离的实用、功利地位,其与世俗王权的相互关系不断发生着改变,社会地位呈持续下降的态势。长江下游文明化进程中宗教信仰的这一变化,事实上是华夏民族早期文明发展中的一般特点。