MCMC方法的发展与现代贝叶斯的复兴——纪念贝叶斯定理发现250周年

信息科学的进步如何影响统计学理论与方法的发展,是21世纪大数据时代统计学面临的重要问题。回顾20世纪40年代MCMC方法的起源与发展,基于千岛湖植物考察与R软件直观性解释Metropolis–Hastings算法,讨论MCMC方法的发展对现代贝叶斯统计复兴具有至关重要的作用。基于云计算随机模拟,统计学与信息科学密切结合、贝叶斯与频率统计相互交融的统计分析新范式,可能成为大数据研究的新思路。     

A Bayesian Analysis of Synchronous Distance Learning versus Matched Traditional Control in Graduate Biostatistics Courses

Distance learning can be useful for bridging geographical barriers to education in rural settings. However, empirical evidence on the equivalence of distance education and traditional face-to-face (F2F) instruction in statistics and biostatistics is mixed. Despite the difficulty in randomization, we minimized intra-instructor variation between F2F and online sections in seven graduate-level biostatistics service courses in a synchronous (live, real time) fashion; that is, for each course taught in a traditional F2F setting, a separate set of students were taught simultaneously via online learning technology, allowing for two-way interaction between instructor and students. Our primary objective was to compare student performance in the two courses that use these two teaching modes. We used a Bayesian hierarchical model to test equivalence of modes. The frequentist mixed model approach was also conducted for reference. The results of Bayesian and frequentist methods agree and suggest a difference of less than 1% in average final grades. Finally, we discuss barriers to instruction and learning using the applied online teaching technology.     

Teaching Elementary Bayesian Statistics with Real Applications in Science

University courses in elementary statistics are usually taught from a frequentist perspective. In this paper I suggest how such courses can be taught using a Bayesian approach, and I indicate why beginning students are well served by a Bayesian course. A principal focus of any good elementary course is the application of statistics to real and important scientific problems. The Bayesian approach fits neatly with a scientific focus. Bayesians take a larger view, and one not limited to data analysis. In particular, the Bayesian approach is subjective, and requires assessing prior probabilities. This requirement forces users to relate current experimental evidence to other available information–-including previous experiments of a related nature, where “related” is judged subjectively. I discuss difficulties faced by instructors and students in elementary Bayesian courses, and provide a sample syllabus for an elementary Bayesian course.     

A nonsymbolic statistics course

A new statistics course Is being taught at the University of Kentucky which does not require students to learn the symbolic language uf statistics (the formulas) Students who will never take a traditional "methods"course in satistics learn to become better consumer of the satistics fed them daily by different news media.other students who realised that munch satistics await them in graduate see this course as a good startingpoint     

Using multivariate rank sum tests to evaluate effectiveness of computer applications in teaching business statistics

Arguments about using computer facilities in classroom teaching have received a lot of attention over time. Using the computer facilities will be helpful to demonstrate real-world applications, while poor data or inappropriate case studies might hinder the applications of the computer programs in classroom teaching. In this paper, we examine the impacts that using computer programs to teach business statistics have on students in the Krannert School of Management at Purdue University. The results show that students are attracted to the interactive computer programs designed for the business statistics course, and students are more motivated to attend classes when computer programs are applied in teaching. Furthermore, computer programs help students to understand confusing topics, and students feel that teaching them to use computer facilities really improves their own abilities to apply similar programs in analyzing real-world problems.     

The current state of Bayesian methods in nonclinical pharmaceutical statistics: Survey results and recommendations from the DIA/ASA-BIOP Nonclinical Bayesian Working Group

The use of Bayesian methods to support pharmaceutical product development has grown in recent years. In clinical statistics, the drive to provide faster access for patients to medical treatments has led to a heightened focus by industry and regulatory authorities on innovative clinical trial designs, including those that apply Bayesian methods. In nonclinical statistics, Bayesian applications have also made advances. However, they have been embraced far more slowly in the nonclinical area than in the clinical counterpart. In this article, we explore some of the reasons for this slower rate of adoption. We also present the results of a survey conducted for the purpose of understanding the current state of Bayesian application in nonclinical areas and for identifying areas of priority for the DIA/ASA-BIOP Nonclinical Bayesian Working Group. The survey explored current usage, hurdles, perceptions, and training needs for Bayesian methods among nonclinical statisticians. Based on the survey results, a set of recommendations is provided to help guide the future advancement of Bayesian applications in nonclinical pharmaceutical statistics.     

在争论中不断发展与完善的统计学

 统计学发展过程中出现过的四次重要的争论。本文围绕着这些争论来展现统计学思想方法发展的历程。国势学与政治算术的争论,明确了统计学的学科性质;描述统计学与推断统计学的争论,建构了统计学的完整体系;经典统计学与贝叶斯统计学争论,带来了新的统计哲学观;信息统计学、经典统计学、贝叶斯统计学之间的争论,推进了统计推断科学化问题的研究。统计学正是通过不同学派之间的争论完善了其思想和方法体系。     

Statistical Computing Packages: Some Words of Caution

Three situations are cited when caution is needed in using statistical computing packages: (a) when analyzing data and having insufficient statistical knowledge to completely understand the output; (b) when teaching the use of packages in a statistics course, to the exclusion of teaching statistics; and (c) when using packages in subject-matter teaching, without teaching the statistical methods underlying the packages.     

适应网络经济的《统计学》教学思考

网络经济的到来,强力冲击着统计工作和统计学。作为经济类和管理类学生专业基础课的《统计学》教学,应该在教学理念、教学内容和教学手段方面适应网络经济。     

贝叶斯统计推断及其主要进展

贝叶斯统计推断作为现代统计分析方法的重要内容,对于统计学理论的发展具有里程碑的作用。深入总结其研究的主要进展,具有重要的现实意义。在查阅国内外重要学术研究资料的基础上,从贝叶斯统计推断的思想、与古典统计的研究思路比较和贝叶斯统计推断研究的主要进展三个方面作了综述与介绍,力图达到认识贝叶斯统计推断及其研究现状的目的。     

A Bayesian approach to sequential analysis in post‐licensure vaccine safety surveillance

With rapid development of computing technology, Bayesian statistics have increasingly gained more attention in various areas of public health. However, the full potential of Bayesian sequential methods applied to vaccine safety surveillance has not yet been realized, despite acknowledged practical benefits and philosophical advantages of Bayesian statistics. In this paper, we describe how sequential analysis can be performed in a Bayesian paradigm in the field of vaccine safety. We compared the performance of the frequentist sequential method, specifically, Maximized Sequential Probability Ratio Test (MaxSPRT), and a Bayesian sequential method using simulations and a real world vaccine safety example. The performance is evaluated using three metrics: false positive rate, false negative rate, and average earliest time to signal. Depending on the background rate of adverse events, the Bayesian sequential method could significantly improve the false negative rate and decrease the earliest time to signal. We consider the proposed Bayesian sequential approach to be a promising alternative for vaccine safety surveillance.     

Teaching statistics to clinical research staff in a pharmaceutical company

Education of clinical research staff in understanding statistical concepts is an area of importance for pharmaceutical companies. This understanding is needed to help them communicate with statisticians using a common language, in designing clinical trials and interpretation of clinical trial results. Such staff has little time for a one-semester or even a one-week continuing education course in statistics. Faced with this reality, we developed a 3-module course,for a total of 1.5 days, which was taught over a period of one month that addresses the needs of this audience. We describe the format and content of the course and provide references that can serve as a resource for teaching such a course.     

A Paradox on Compartmental Models with Poisson Immigration

Even to the initiated, statistical calculations based on Bayes's Theorem can be daunting because of the numerical integrations required in all but the simplest applications. Moreover, from a teaching perspective, introductions to Bayesian statistics—if they are given at all—are circumscribed by these apparent calculational difficulties. Here we offer a straightforward sampling-resampling perspective on Bayesian inference, which has both pedagogic appeal and suggests easily implemented calculation strategies.     

Bias in Routine Calculation of the Variance of OLS Estimators When the Disturbances are Autocorrelated

In this article a sequence of statistical games is described that were found useful for teaching statistics to agriculture students. The ideas of experimental design tend to be neglected in statistics service courses for agriculturalists because of the practical difficulty of allowing students to learn design by experience. Simulating experiments in the classroom or on the computer console is a viable alternative and should be more widely used. In this article, three games—TOMATO, CHICK, and SELECT—are described. Other games can be invented. The relevance of using games extends to fields other than agriculture.     

The stein effect and bayesian analysis: a reexamination

The Stein, that one could improve frequentist risk by combining “independent” problems, has long been an intriguing paradox to statistics. We briefly review the Bayesian view of the paradox, and indicate that previous justifications of the Stein effect, through concerns of “Bayesian robustness,” were misleading. In the course of doing so, several existing robust Bayesian and Stein-effect estimators are compared for a variety of situations.     

Considerate approaches to constructing summary statistics for ABC model selection

For nearly any challenging scientific problem evaluation of the likelihood is problematic if not impossible. Approximate Bayesian computation (ABC) allows us to employ the whole Bayesian formalism to problems where we can use simulations from a model, but cannot evaluate the likelihood directly. When summary statistics of real and simulated data are compared??rather than the data directly??information is lost, unless the summary statistics are sufficient. Sufficient statistics are, however, not common but without them statistical inference in ABC inferences are to be considered with caution. Previously other authors have attempted to combine different statistics in order to construct (approximately) sufficient statistics using search and information heuristics. Here we employ an information-theoretical framework that can be used to construct appropriate (approximately sufficient) statistics by combining different statistics until the loss of information is minimized. We start from a potentially large number of different statistics and choose the smallest set that captures (nearly) the same information as the complete set. We then demonstrate that such sets of statistics can be constructed for both parameter estimation and model selection problems, and we apply our approach to a range of illustrative and real-world model selection problems.     

Dempster's combination rule and sufficient statistics

In his articles (1966-1968) concerning statistical inference based on lower and upper probabilities, Dempster refers to the connection between Fisher's fiducial argument and his own ideas of statistical inference. Dempster's main concern however focuses on the “Bayesian” aspects of his theory and not on an elaboration of the relation between Fisher's and his ideas. This article attempts to work out the connection between those two approaches and focuses primarily on the question, whether Dempster's combination rule, his upper and lower probabilty based on sufficient statistics and inference based on sufficient statistics in Fisher's sense are consistent. To be adequate to Fisher's reasoning, we deal with absolutely continuous, one parametric families of distributions.This is certainly not the usual assumption in context with Dempster's theory and implies a normative but straightforward definition concerning the underlying conditional distribution; this definition however is done in Dempster's spirit as can be seen from his articles, (1966, 1968,a,b). Under those assumptions it can be shown that - similar to Lindley's results concerning consistency in fiducial reasoning (1958) - the combination rule, Dempster's procedure based on sufficient statistics and fiducial inference by sufficient statistics agree iff the parametric family under consideration can be transformed to location parameter form.     

Teaching Regressions an Exploratory Approach

An applied statistics and data-analysis course designed for students of public management and policy analysis, but suitable as an introductory graduate-level applied course in other contexts, is discussed. The course, Quantitative Methods for Public Management (QMPM), is a departure from traditional instruction in statistics. It uses subject-matter hierarchies to schedule the presentation of substantive material, and it integrates exploratory data analysis (EDA) and standard classical techniques. This integration is accomplished by using exploratory methods to clarify and evaluate analyses performed with classical procedures. The course, taught since 1975 at Carnegie-Mellon University's School of Urban and Public Affairs, has been evaluated experimentally through a randomized assignment of students to either a traditional introductory statistics course or QMPM. We concentrate here on the QMPM approach to teaching regression.     

Non-linear regression models for Approximate Bayesian Computation

Approximate Bayesian inference on the basis of summary statistics is well-suited to complex problems for which the likelihood is either mathematically or computationally intractable. However the methods that use rejection suffer from the curse of dimensionality when the number of summary statistics is increased. Here we propose a machine-learning approach to the estimation of the posterior density by introducing two innovations. The new method fits a nonlinear conditional heteroscedastic regression of the parameter on the summary statistics, and then adaptively improves estimation using importance sampling. The new algorithm is compared to the state-of-the-art approximate Bayesian methods, and achieves considerable reduction of the computational burden in two examples of inference in statistical genetics and in a queueing model.     

A Bayesian approach to the statistical analysis of device preference studies

Drug delivery devices are required to have excellent technical specifications to deliver drugs accurately, and in addition, the devices should provide a satisfactory experience to patients because this can have a direct effect on drug compliance. To compare patients' experience with two devices, cross-over studies with patient-reported outcomes (PRO) as response variables are often used. Because of the strength of cross-over designs, each subject can directly compare the two devices by using the PRO variables, and variables indicating preference (preferring A, preferring B, or no preference) can be easily derived. Traditionally, methods based on frequentist statistics can be used to analyze such preference data, but there are some limitations for the frequentist methods. Recently, Bayesian methods are considered an acceptable method by the US Food and Drug Administration to design and analyze device studies. In this paper, we propose a Bayesian statistical method to analyze the data from preference trials. We demonstrate that the new Bayesian estimator enjoys some optimal properties versus the frequentist estimator.