Properties of Bayes Factors Based on Test Statistics

Abstract.  This article examines the consistency, interpretation and application of Bayes factors constructed from standard test statistics. Primary conclusions are that Bayes factors based on multinomial and normal test statistics are consistent for suitable choices of the hyperparameters used to specify alternative hypotheses, and that such constructions can be extended to obtain consistent Bayes factors based on likelihood ratio statistics. A connection between Bayes factors based on likelihood ratio statistics and the Bayesian information criterion is exposed, as is a connection between Bayes factors based on F statistics and parametric Bayes factors based on normal-inverse gamma models. Similarly, Bayes factors based on chi-squared statistics for multinomial data are shown to provide accurate approximations to Bayes factors based on multinomial/Dirichlet models. An illustration of how the simple form of these Bayes factors can be exploited to generate easily interpretable summaries of the experimental 'weight of evidence' is provided.     

Theory & Methods: Why do we do it? Statisticians and the Practice of Statistics

There has been no work done on why statisticians have chosen their particular profession. With the increasing emphasis on the development of biotechnology, it seems important to encourage people to take up statistics and to offer the perspective that the study of statistics brings. This paper is an attempt to develop a preliminary understanding, by open-ended in-depth interviewing, of the personal backgrounds that have encouraged present practising statisticians to move into this field, and to see how they experience their work.     

On Bayes Linear Unbiased Estimator Under the Balanced Loss Function

In this paper, the Bayes linear unbiased estimator (Bayes LUE) is derived under the balanced loss function. Moreover, the superiority of Bayes LUE over ordinary least square estimator is studied under the mean square error matrix criterion and Pitman closeness criterion. Furthermore, we compare Bayes LUE under the balanced loss function with Bayes LUE under the quadratic loss function.     

Teaching Statistics Theory through Applications

This article presents a model for developing case studies, or labs, for use in undergraduate mathematical statistics courses. The model proposed here is to design labs that are more in-depth than most examples in statistical texts by providing rich background material, investigations and analyses in the context of a scientific problem, and detailed theoretical development within the lab. An important goal of this approach is to encourage and develop statistical thinking. It is also advocated that the labs be made the centerpiece of the theoretical course. As a result, the curriculum, lectures, and assignments are significantly restructured. For example, the course work includes written assignments based on open-ended data analyses, and the lectures include group work and discussions of the case-studies.     

Teaching Bayesian Statistics Using Sampling Methods and MINITAB

Bayesian statistics can be hard to teach at an elementary level due to the difficulty in deriving the posterior distribution for interesting nonconjugate problems. One attractive method of summarizing the posterior distribution is to directly simulate from the probability distribution of interest and then explore the simulated sample. We illustrate the use of Rubin's Sampling-Importance-Resampling (SIR) algorithm to simulate posterior distributions for three inference problems. In each example, we focus on the construction of the prior distribution and then use exploratory data analysis techniques to describe the posterior samples and make inferences. The use of MINITAB macros is presented to illustrate the ease of performing this simulation on standard statistical computer programs.     

An Introduction to Modern Matrix Methods and Statistics

In this article, using the representation that the Kalman filter recursions in state-space models can be expressed as a matrix-weighted average of prior and sample estimates, we supplement the usual filtering algorithm by an extreme bounds analysis. Specifically, as the covariance matrix of the state error is varied in the class of symmetric and positive-definite matrices, the filtering estimates are shown to be in an ellipsoid.     

Applying Cognitive Theory to Statistics Instruction

This article presents five principles of learning, derived from cognitive theory and supported by empirical results in cognitive psychology. To bridge the gap between theory and practice, each of these principles is transformed into a practical guideline and exemplified in a real teaching context. It is argued that this approach of putting cognitive theory into practice can offer several benefits to statistics education: A means for explaining and understanding why reform efforts work; a set of guidelines that can help instructors make well-informed design decisions when implementing these reforms; and a framework for generating new and effective instructional innovations.     

统计数据质量评估方法研究述评

数据质量评估是统计数据质量管理的重要环节。统计数据质量的评估方法有逻辑关系检验法、计量模型分析法、核算数据重估法、统计分布检验法、调查误差评估法以及多维评估法六个类别,在详细讨论其各自的评估过程、适用性及其优缺点的基础上,按照评估维度和评估方式对各种统计数据质量的评估方法进行再归类,指出评估方法的进一步研究应该围绕计量模型分析法、核算数据重估法中的物量指数重估法、调查误差评估法和多维评估法等方向展开。     

企业研发投入:政府统计与企业会计核算方法比较

企业是实施研发活动的最重要主体,夯实企业研发投入数据关系到国家研发投入统计和核算,关系到对企业创新能力的判断.本文从概念定义、指标设置、核算实务等层面,对政府统计和企业会计围绕企业研发支出数据形成过程做系统比较,并延伸到国民经济核算的处理方式.研究表明:第一,当前企业研发支出会计核算有比较明显的功利色彩,从覆盖的企业面、数据的客观性等方面考虑,尚不能与政府研发支出统计衔接;第二,政府研发支出统计内容及形成指标尚比较有限,有待于进一步扩展以便为国民经济核算提供更有力的支持.     

线性无量纲化方法比较研究

根据线性无量纲化方法函数构成所使用的中心点值和值域指标以及其斜率和截距的表达式,对8种线性无量纲化方法进行分析,从不同的角度再次论证不同线性无量纲化方法所满足的性质定理,并进行了理论论证。同时,通过对线性无量纲化方法的分类比较,结合相关性质定理提出了多种线性无量纲化方法,并说明了其相关性质,具有一定的科学性。同时还分析了在对多指标数据进行综合评价的过程中只采用一种线性无量纲化方法的不足,提出了采用多种无量纲化方法的设想的理论可行性,并用案例进行了实证分析,表明其存在一定的合理性。