Showing papers in "Statistical Science in 1990"
TL;DR: Neyman as mentioned in this paper introduced a model for the analysis of field experiments conducted for the purpose of comparing a number of crop varieties, which makes use of a double-indexed array of unknown potential yields, one index corresponding to varieties and the other to plots.
Abstract: In the portion of the paper translated here, Neyman introduces a model for the analysis of field experiments conducted for the purpose of comparing a number of crop varieties, which makes use of a double-indexed array of unknown potential yields, one index corresponding to varieties and the other to plots The yield corresponding to only one variety will be observed on any given plot, but through an urn model embodying sampling without replacement from this doubly indexed array, Neyman obtains a formula for the variance of the difference between the averages of the observed yields of two varieties This variance involves the variance over all plots of the potential yields and the correlation coefficient $r$ between the potential yields of the two varieties on the same plot Since it is impossible to estimate $r$ directly, Neyman advises taking $r = 1$, observing that in practice this may lead to using too large an estimated standard deviation, when comparing two variety means
1,627 citations
1,428 citations
TL;DR: The Chen-Stein method of Poisson approximation is a powerful tool for computing an error bound when approximating probabilities using the Poisson distribution as discussed by the authors, in many cases, this bound may be given in terms of first and second moments alone.
Abstract: The Chen-Stein method of Poisson approximation is a powerful tool for computing an error bound when approximating probabilities using the Poisson distribution. In many cases, this bound may be given in terms of first and second moments alone. We present a background of the method and state some fundamental Poisson approximation theorems. The body of this paper is an illustration, through varied examples, of the wide applicability and utility of the Chen-Stein method. These examples include birthday coincidences, head runs in coin tosses, random graphs, maxima of normal variates and random permutations and mappings. We conclude with an application to molecular biology. The variety of examples presented here does not exhaust the range of possible applications of the Chen-Stein method.
333 citations
TL;DR: This paper reviews and critique various statistical approaches that have been proposed for the design and analysis of sequential experiments in medical applications, including group sequential tests, stochastic curtailment, repeated confidence intervals, and Bayesian procedures.
Abstract: Most medical trials are monitored for early evidence of treatment differences or harmful side effects. In this paper we review and critique various statistical approaches that have been proposed for the design and analysis of sequential experiments in medical applications. We discuss group sequential tests, stochastic curtailment, repeated confidence intervals, and Bayesian procedures. The role that a statistical stopping rule should play in the final analysis is examined.
168 citations
TL;DR: For 20 different studies, Table 1 tabulates numerical averages of opinions on quantitative meanings of 52 qualitative probabilistic expres- sions as discussed by the authors, and the effect of modifiers such as very or negation (not, un-, im-, in-) can be described by a simple rule.
Abstract: For 20 different studies, Table 1 tabulates numerical averages of opinions on quantitative meanings of 52 qualitative probabilistic expres- sions. Populations with differing occupations, mainly students, physicians, other medical workers, and science writers, contributed. In spite of the variety of populations, format of question, instructions, and context, the variation of the averages for most of the expressions was modest, suggesting that they might be useful for codification. One exception was possible, because it had distinctly different meanings for different people. We report new data from a survey of science writers. The effect of modifiers such as very or negation (not, un-, im-, in-) can be described approximately by a simple rule. The modified expression has probability meaning half as far from the appropriate boundary (0 or 100) as that of the original expression. This paper also reviews studies that show stability of meanings over 20 years, mild effects of translation into other languages, context, small order effects, and effects of scale for reporting on extreme values. The stem probability with modifiers gives a substantial range 6% to 91% and the stem chance might do as well if tried with very. The stems frequent, probable, likely, and often with modifiers produce roughly equivalent sets of means, but do not cover as wide a range as probability. Extreme values such as always and certain fall at 98% and 95%, respectively, and impossible and never at 1%. The next step will be to offer codifications and see how satisfactory people find them.
167 citations
TL;DR: A number of distinct roles are identified for probability models used in the analysis of data and some general issues arising in the formulation of such models are discussed.
Abstract: A number of distinct roles are identified for probability models used in the analysis of data. Examples are outlined. Some general issues arising in the formulation of such models are discussed.
158 citations
TL;DR: In this paper, a distinction between two types of models (empirical and explanatory) has been discussed by Neyman, Box, and others, and some lines of further work has been considered.
Abstract: Since Fisher’s formulation in 1922 of a framework for theoretical statistics, statistical theory has been concerned primarily with the derivation and properties of suitable statistical procedures on the basis of an assumed statistical model (including sensitivity to deviations from this model). Until relatively recently, the theory has paid little attention to the question of how such a model should be chosen. In the present paper, we consider first what Fisher and Neyman had to say about this problem and in Section 2 survey some contributions statistical theory has made to it. In Section 3 we study a distinction between two types of models (empirical and explanatory) which has been discussed by Neyman, Box, and others. A concluding section considers some lines of further work.
129 citations
TL;DR: The concept of predictive likelihood is reviewed and studied in this paper, where the emphasis is on comparing and clarifying some of the more important predictive likelihoods suggested in the literature and a unified modification and simplification of the sufficiency-based predictive likelihood models is sug- gested.
Abstract: The concept of predictive likelihood is reviewed and studied. The emphasis is on comparing and clarifying some of the more important predictive likelihoods suggested in the literature. A unified modification and simplification of the sufficiency-based predictive likelihoods is sug- gested. Other predictive likelihoods discussed include the profile predictive likelihood and various modifications of it.
127 citations
123 citations
TL;DR: The computer-mainly as display maker, but significantly as number cruncher- has so greatly enhanced their potentialities that the authors have much to explore and many important steps to take.
Abstract: Visual display based on data deserves careful attention to a long list of ideas and questions (19 are discussed below). While classical views of graphical display need to be re-examined and selectively used, the computer-mainly as display maker, but significantly as number cruncher- has so greatly enhanced our potentialities that we have much to explore and many important steps to take. In particular, we need to pay serious and continuing attention to securing: (a) immediate and strong impact, (b) easy flow of attention across parallel elements, (c) planning to show phe- nomena, not numbers, (d) attention to both prospecting for what the data might show and transfer (to others) of what we have learned from it, (e) partnership with computation, and (f) putting disproportionate response to work. The next decade or two should see major advances.
122 citations
TL;DR: The first five sections of the paper describe the Bayesian paradigm for statistics and its relationship with other attitudes towards inference and an attempt is made to appreciate how accurate formulae like the extension of the conversation, the product law and Bayes rule are in evaluating probabilities.
Abstract: The first five sections of the paper describe the Bayesian paradigm for statistics and its relationship with other attitudes towards inference. Section 1 outlines Wald's major contributions and explains how they omit the vital consideration of coherence. When this point is included the Bayesian view results, with the main difference that Waldean ideas require the concept of the sample space, whereas the Bayesian approach may dispense with it, using a probability distribution over parameter space instead. Section 2 relates statistical ideas to the problem of inference in science. Scientific inference is essentially the passage from observed, past data to unobserved, future data. The roles of models and theories in doing this are explored. The Bayesian view is that all this should be accomplished entirely within the calculus of probability and Section 3 justifies this choice by various axiom systems. The claim is made that this leads to a quite different paradigm from that of classical statistics and, in particular, prob- lems in the latter paradigm cease to have importance within the other. Point estimation provides an illustration. Some counter-examples to the Bayesian view are discussed. It is important that statistical conclusions should be usable in making decisions. Section 4 explains how the Bayesian view achieves this practi- cality by introducing utilities and the principle of maximizing expected utility. Practitioners are often unhappy with the ideas of basing inferences on one number, probability, or action on another, an expectation, so these points are considered and the methods justified. Section 5 discusses why the Bayesian viewpoint has not achieved the success that its logic suggests. Points discussed include the relationship between the inferences and the practical situation, for example with multiple comparisons; and the lack of the need to confine attention to normality or the exponential family. Its extensive use by nonstatisticians is documented. The most important objection to the Bayesian view is that which rightly says that probabilities are hard to assess. Consequently Section 6 considers how this might be done and an attempt is made to appreciate how accurate formulae like the extension of the conversation, the product law and Bayes rule are in evaluating probabilities.
TL;DR: In this paper, the authors examined Stein's paradox from the perspective of an earlier century and showed that from that point of view the phenomenon is transparent, and this earlier perspective leads to a relatively simple rigorous proof of Stein's result and the perspective can be extended to cover other situations, such as the simultaneous estimation of several Poisson means.
Abstract: More than 30 years ago, Charles Stein discovered that in three or more dimensions, the ordinary estimator of the vector of means of a multivariate normal distribution is inadmissible. This article examines Stein's paradox from the perspective of an earlier century and shows that from that point of view the phenomenon is transparent. Furthermore, this earlier perspective leads to a relatively simple rigorous proof of Stein's result, and the perspective can be extended to cover other situations, such as the simultaneous estimation of several Poisson means. The relationship of this perspective to other earlier work, including the empirical Bayes approach, is also discussed.
TL;DR: In this paper, the authors trace the history of the problem of estimating the variance, σ 2, based on a random sample from a normal distribution with mean σ σ$ unknown.
Abstract: This article traces the history of the problem of estimating the variance, $\sigma^2$, based on a random sample from a normal distribution with mean $\mu$ unknown. Considered are both the point estimation and confidence interval cases. We see that improvement over both usual estimators follows a remarkably parallel development and stemmed from the innovative ideas presented in Stein (1964). We examine developments through the most recent dealing with improved confidence intervals and conditional evaluations of interval estimators.
TL;DR: Bayesian methods simplify the analysis of data from sequential clinical trials and avoid certain paradoxes of frequentist inference, and offer a natural setting for the synthesis of expert opinion in deciding policy matters.
Abstract: Attitudes of biostatisticians toward implementation of the Bayesian paradigm have changed during the past decade due to the increased availability of computational tools for realistic problems. Empirical Bayes' methods, already widely used in the analysis of longitudinal data, promise to improve cancer incidence maps by accounting for overdispersion and spatial correlation. Hierarchical Bayes' methods offer a natural framework in which to demonstrate the bioequivalence of pharmacologic compounds. Their use for quantitative risk assessment and carcinogenesis bioassay is more controversial, however, due to uncertainty regarding specification of informative priors. Bayesian methods simplify the analysis of data from sequential clinical trials and avoid certain paradoxes of frequentist inference. They offer a natural setting for the synthesis of expert opinion in deciding policy matters. Both frequentist and Bayes' methods have a place in biostatistical practice.
TL;DR: In this paper, the authors present an expository development of Stein estimation with substantial emphasis on exact results for spherically symmetric distributions, showing that the improvement possible over the best invariant estimator via shrinkage estimation is not surprising but expected from a variety of perspectives.
Abstract: This paper presents an expository development of Stein estimation with substantial emphasis on exact results for spherically symmetric distributions. The themes of the paper are: a) that the improvement possible over the best invariant estimator via shrinkage estimation is not surprising but expected from a variety of perspectives; b) that the amount of shrinkage allowable to preserve domination over the best invariant estimator is, when properly interpreted, relatively free from the assumption of normality; and c) that the potential savings in risk are substantial when accompanied by good quality prior information.
TL;DR: Mathematical probability and its child, mathematical statistics, are relative newcomers on the intellectual scene as mentioned in this paper, and they have acquired a dazzling range of applications inside the university, we see them taught and used in a remarkable range of disciplines.
Abstract: Mathematical probability and its child, mathematical statistics, are relative newcomers on the intellectual scene. Mathematical probability was invented in 1654 by two Frenchman, Blaise Pascal and Pierre Fermat. Mathematical statistics emerged from the work of the continental mathematicians Gauss and Laplace in the early 1800s, and it became widely useful only in this century, as the result of the work of three Englishmen, Francis Galton, Karl Pearson, and R.A. Fisher. In spite of these late beginnings, probability and statistics have acquired a dazzling range of applications. Inside the university, we see them taught and used in a remarkable range of disciplines. Statistics is used routinely in engineering, business, and medicine, and in every social and natural science. It is making inroads in law and in the humanities. Probability, aside from its use in statistical theory, is finding new applications in engineering, computer science, economics, psychology, and philosophy.
TL;DR: In this paper, the similarities and differences in Playfair and Tukey's visions of what graphically displaying quantitative phenomena can do now and might do in the future are discussed, and five important areas of current and future graphic concern are discussed.
Abstract: This paper discusses the similarities and differences in Playfair and Tukey's visions of what graphically displaying quantitative phenomena can do now, and might do in the future. As part of this discussion we examine: (1) how fundamental graphic tools have become to the scientist, (2) three instances where modern views of graphics are unchanged since Playfair's time, and (3) one area where there has been a change. The paper concludes with a discussion of five important areas of current and future graphic concern.
TL;DR: Playfair's understanding of the psychology of the graphic method was remarkable; there was an inner coherence to his picture of the reader's psychological needs which is strikingly modern.
Abstract: William Playfair is a key figure in the history of quantitative graphics. He was a popularizer and propagandist, a prolific designer of charts, and a developer of economic and business graphics. He established the line graph (especially the simple surface chart) as an important alternative to the table for the nonspecialist reader. Although his charts were not quite so original as some have supposed, they do contain graphic design ideas of great interest and occasional brilliance. His Commercial and Political Atlas of 1786 was a notable venture; it began his 36-year career as a graphic communicator. Playfair's understanding of the psychology of the graphic method was remarkable; there was an inner coherence to his picture of the reader's psychological needs which is strikingly modern (the paper contains excerpts from his many publications).
TL;DR: A strategy for online multivariate exploratory graphical analysis is presented and illustrated, motivated by the need for a routine procedure for searching for structure in multivariate data sets arising in the context of a major pharmaceutical, dyestuffs and agrochemical company.
Abstract: A strategy for online multivariate exploratory graphical analysis is presented and illustrated, motivated by the need for a routine procedure for searching for structure in multivariate data sets arising in the context of a major pharmaceutical, dyestuffs and agrochemical company.
TL;DR: Only with understanding of statistical variability can managers distinguish special from common causes of variation, intelligently direct efforts to improve processes, and avoid the tampering that can make processes worse.
Abstract: Statistical methodology has great potential for useful application in business, but that potential is seldom realized However, companies are increasingly exploiting simple statistical tools in quality and productivity improvement and developing "company cultures" congenial to effective use of statistics Statistical and probabilistic thinking is essential for sound decision-making Only with understanding of statistical variability can managers distinguish special from common causes of variation, intelligently direct efforts to improve processes, and avoid the tampering that can make processes worse Statistics can be used most effectively in business when many employees--"parastatisticians"--have some grasp of statistical tools and thinking Fortunately, there is evidence that very elementary tools suffice to make rough-and-ready studies that can illuminate most business problems and facilitate most decisions