Showing papers in "Statistical Science in 1992"

Inference from Iterative Simulation Using Multiple Sequences

Abstract: The Gibbs sampler, the algorithm of Metropolis and similar iterative simulation methods are potentially very helpful for summarizing multivariate distributions. Used naively, however, iterative simulation can give misleading answers. Our methods are simple and generally applicable to the output of any iterative simulation; they are designed for researchers primarily interested in the science underlying the data and models they are analyzing, rather than for researchers interested in the probability theory underlying the iterative simulations themselves. Our recommended strategy is to use several independent sequences, with starting points sampled from an overdispersed distribution. At each step of the iterative simulation, we obtain, for each univariate estimand of interest, a distributional estimate and an estimate of how much sharper the distributional estimate might become if the simulations were continued indefinitely. Because our focus is on applied inference for Bayesian posterior distributions in real problems, which often tend toward normality after transformations and marginalization, we derive our results as normal-theory approximations to exact Bayesian inference, conditional on the observed simulations. The methods are illustrated on a random-effects mixture model applied to experimental measurements of reaction times of normal and schizophrenic patients.

Practical Markov Chain Monte Carlo

Abstract: Markov chain Monte Carlo using the Metropolis-Hastings algorithm is a general method for the simulation of stochastic processes having probability densities known up to a constant of proportionality. Despite recent advances in its theory, the practice has remained controversial. This article makes the case for basing all inference on one long run of the Markov chain and estimating the Monte Carlo error by standard nonparametric methods well-known in the time-series and operations research literature. In passing it touches on the Kipnis-Varadhan central limit theorem for reversible Markov chains, on some new variance estimators, on judging the relative efficiency of competing Monte Carlo schemes, on methods for constructing more rapidly mixing Markov chains and on diagnostics for Markov chain Monte Carlo.

A Survey of Exact Inference for Contingency Tables

Abstract: The past decade has seen substantial research on exact infer- ence for contingency tables, both in terms of developing new analyses and developing efficient algorithms for computations. Coupled with concomitant improvements in computer power, this research has re- sulted in a greater variety of exact procedures becoming feasible for practical use and a considerable increase in the size of data sets to which the procedures can be applied. For some basic analyses of contin- gency tables, it is unnecessary to use large-sample approximations to sampling distributions when their adequacy is in doubt. This article surveys the current theoretical and computational developments of exact methods for contingency tables. Primary attention is given to the exact conditional approach, which eliminates nuisance parameters by conditioning on their sufficient statistics. The presentation of various exact inferences is unified by expressing them in terms of parameters and their sufficient statistics in loglinear models. Exact approaches for many inferences are not yet addressed in the literature, particularly for multidimensional contingency tables, and this article also suggests additional research for the next decade that would make exact methods yet more widely applicable.

Statistical methods for data with long-range dependence

Abstract: It is well known to applied statisticians and scientists that the assumption of independence is often not valid for real data. In particular, even when all precautions are taken to prevent dependence, slowly decaying serial correlations frequently occur. If not taken into account, they can have disastrous effects on statistical inference. This phenomenon has been observed empirically by many prominent scientists long before suitable mathematical models were known. Apart from some scattered early references, mathematical models with long-range dependence were first introduced to statistics by Mandelbrot and his co-workers (Mandelbrot and Wallis, 1968, 1969; Mandelbrot and van Ness, 1968). Since then, long-range dependence in statistics has gained increasing attention. Parsimonious models with long memory are stationary increments of self-similar processes with self-similarity parameter $H \in (1/2,1)$, fractional ARIMA processes and other stationary stochastic processes with non-summable correlations. In the last decade, many results on statistical inference for such processes have been established. In the present paper, a review of these results is given.

Modeling publication selection effects in meta-analysis

Abstract: Publication selection effects arise in meta-analysis when the effect magnitude estimates are observed in (available from) only a subset of the studies that were actually conducted and the probability that an estimate is observed is related to the size of that estimate. Such selection effects can lead to substantial bias in estimates of effect magnitude. Research on the selection process suggests that much of the selection occurs because researchers, reviewers and editors view the results of studies as more conclusive when they are more highly statistically significant. This suggests a model of the selection process that depends on effect magnitude via the p-value or significance level. A model of the selection process involving a step function relating the p-value to the probability of selection is introduced in the context of a random effects model for meta-analysis. The model permits estimation of a weight function representing selection along the mean and variance of effects. Some ideas for graphical procedures and a test for publication selection are also introduced. The method is then applied to a meta-analysis of test validity studies.

An Approach for Assessing Publication Bias Prior to Performing a Meta-Analysis

Abstract: A semi-parametric method is developed for assessing publication bias prior to performing a meta-analysis. Summary estimates for the individual studies in the meta-analysis are assumed to have known distributional form. Selective publication is modeled using a nonparametric weight function, defined on the two-sided p-value scale. The shape of the estimated weight function provides visual evidence of the presence of bias, if it exists, and observed trends may be tested using rank order statistics or likelihood ratio tests. The method is intended as an exploratory technique prior to embarking on a standard meta-analysis.

R. A. Fisher and Fiducial Argument

Abstract: The fiducial argument arose from Fisher's desire to create an inferential alternative to inverse methods. Fisher discovered such an alternative in 1930, when he realized that pivotal quantities permit the derivation of probability statements concerning an unknown parameter independent of any assumption concerning its a priori distribution. The original fiducial argument was virtually indistinguishable from the confidence approach of Neyman, although Fisher thought its application should be restricted in ways reflecting his view of inductive reasoning, thereby blending an inferential and a behaviorist viewpoint. After Fisher attempted to extend the fiducial argument to the multiparameter setting, this conflict surfaced, and he then abandoned the unconditional sampling approach of his earlier papers for the conditional approach of his later work. Initially unable to justify his intuition about the passage from a probability assertion about a statistic (conditional on a parameter) to a probability assertion about a parameter (conditional on a statistic), Fisher thought in 1956 that he had finally discovered the way out of this enigma with his concept of recognizable subset. But the crucial argument for the relevance of this concept was founded on yet another intuition--one which, now clearly stated, was later demonstrated to be false by Buehler and Feddersen in 1963.

Multilinear Models: Applications in Spectroscopy

Abstract: Multilinear models are models in which the expectation of a multiway array is the sum of products of parameters, where each parame- ter is associated with only one of the ways. In spectroscopy, multilinear models permit mathematical decompositions of data sets when chemical decomposition of specimens is difficult or impossible. This paper presents a unified description of the models in an array notation. The spectroscopic context shows how to interpret one initialization of the nonlinear least- squares fits of these models. Several examples show that these models can be applied successfully.

Statistics, Probability and Chaos

Abstract: The study of chaotic behavior has received substantial attention in many disciplines. Although often based on deterministic models, chaos is associated with complex, "random" behavior and forms of unpredictability. Mathematical models and definitions associated with chaos are reviewed. The relationship between the mathematics of chaos and probabilistic notions, including ergodic theory and uncertainty modeling, are emphasized. Popular data analytic methods appearing in the literature are discussed. A major goal of this article is to present some indications of how probability modelers and statisticians can contribute to analyses involving chaos.

Chaos, Fractals and Statistics

Abstract: We review a wide variety of applications in different branches of sciences arising from the study of dynamical systems. The emergence of chaos and fractals from iterations of simple difference equations is discussed. Notions of phase space, contractive mapping, attractor, in- variant density and the relevance of ergodic theory for studying dynam- ical systems are reviewed. Various concepts of dimensions and their relationships are studied, and their use in the measurement of chaotic phenomena is investigated. We discuss the implications of the growth of nonlinear science on paradigms of model building in the tradition of classical statistics. The role that statistical science can play in future developments of nonlinear science and its possible impact on the future development of statistical science itself are addressed.

Some Progress and Problems in Meta-Analysis of Clinical Trials

Abstract: We report progress on some methodological issues in meta-analysis. Evidence continues to accumulate that randomized trials show smaller gains than nonrandomized trials when innovations are compared to standard therapies. Quality scores for randomized clinical trials show that reporting has improved about 27% in three decades, to a quality level slightly over 50%. Although quality scoring could be useful, in principle, for adjusting estimates of gain from innovations, a substantial study has not found a statistical relation between gains and quality. We describe a method of blinding papers to reduce the bias of readers doing meta-analyses. For combining data for fixed effects, Greenland and Salvan recommend using Mantel-Haensztel, weighted least squares or maximum likelihood methods. For random effects, Larholt, Tsiatis and Gelber have improvements for the DerSimonian and Laird method. Eddy and his colleagues have prepared software and book-length works on Bayesian methods for technology assessment using meta-analysis. Louis has a valuable review article on Bayesian approaches. The annoying difficulties in combining $2 \times 2$ tables when some cells have zeros has been largely overcome by exact calculation methods. From diagnostic data acquired from several independent investigations, new methods have appeared for estimating receiver operating characteristic curves. An update on meta-analyses of randomized clinical trials shows about 16 meta-analyses per year in journals during 1983-1990. We expect much more methodologic work as new issues appear and findings point us toward fresh solutions.

Evaluating Therapeutic Interventions: Some Issues and Experiences

Abstract: In frequently occurring life-threatening diseases such as cancer, AIDS and cardiovascular disease, there is a need of significant public health importance for rapid yet reliable evaluation of promising new therapeutic interventions that might provide greater efficacy and reduced toxicity. Leadership from statistical scientists is essential to effectively address many of the challenges resulting from this need. By discussing recent experiences, primarily in the area of oncology and AIDS clinical trials, we will illustrate several of these challenges. We also will review some designs and methods that have been implemented in these settings. Particular attention will be given to experiences from involvement with FDA Advisory Committees and with Data Monitoring Committees for clinical trials sponsored by industry or by the National Institutes of Health. Among issues to be discussed will be the role of independent monitoring committees and group sequential guidelines in randomized clinical trials, the evaluation of equivalence trials and the use of surrogate and auxiliary endpoints.

R. A. Fisher's Fiducial Argument and Bayes' Theorem

Abstract: I am a logician and a philosopher; I have not studied statistics for very long, and so I still very quickly get out of my depth in a discussion of the technicalities of statistical inference. But I think it is important, none the less, for people whose interests lie in the area of inference as such to do the best they can in reacting to and in having an action upon -current work in that particular kind of inference called "statistical." That this interaction is difficult for both parties is the more reason for attempting it. (p. 938)

R. A. Fisher: The Founder of Modern Statistics

Abstract: Before the beginning of this century, statistics meant ob- served data and descriptive summary figures, such as means, variances, indices, etc., computed from data. With the introduction of the x2 test for goodness of fit (specification) by Karl Pearson (1900) and the t test by- Gosset (Student, 1908) for drawing inference on the mean of a normal population, statistics started acquiring new meaning as a method of processing data to determine the amount of uncertainty in various generalizations we may make from observed data (sample) to the source of the data (population). The major steps that led to the establishment and recognition of statistics as a separate scientific discipline and an inevitable tool in improving natural knowledge were made by R. A. Fisher during the decade 1915-1925. Most of the concepts and methods introduced by Fisher are fundamental and continue to provide the framework for the discussion of statistical theory. Fisher's work is monumental, both in richness and variety of ideas, and provided the inspiration for phenome- nal developments in statistical methodology for applications in all areas of human endeavor during the last 75 years. Some of Fisher's pioneering works have raised bitter controversies that still continue. These controversies have indeed helped in highlight- ing the intrinsic difficulties in inductive reasoning and seeking refine- ments in statistical methodology.

A Brief History of Statistics in Three and One-Half Chapters: A Review Essay

Abstract: This article by Stephen Fienberg reviews the last three and one-half centuries of statistics and probability largely through the author's overview and synthesis of seven recent books on the topic. It is an altering and expansion of an earlier paper with the same title published in Historical Methods. We are partly taking this liberty because Historical Methods falls well outside the normal reading range of statisticians. An extension particularly worth noting is the introductory timeline on pages 210 and 211. The original version appeared in Historical Methods (1991 24 124-135; Heldret Publications, 1319 18th Street, N.W., Washington, D.C. 20036-1802, copyright 1991). Permission to reprint in revised form has been granted by the Helen Dwight Reid Educational Foundation. The seven books reviewed here are as follows:

The Impact of Sociological Methodology on Statistical Methodology

Abstract: Developments in sociological methodology and in quantitative sociology have always been closely related to developments in statistical theory, methodology and computation. The same statement applies if "methodology for social research" and "quantitative social research" re- place the more specific terms in this statement. Statistical methodology, including especially the battery of methods used to estimate and evaluate statistical models, has had a tremendous effect on social research in the post-war period, particularly in the United States. What is less well appreciated is the influence of sociological methodology, or methodology for social research more generally, on modern statistics. I give a brief sketch of the linkages between methodology in social research and meth- odology in statistics. The focus is on areas where developments in sociological methodology, or at least the scientific contexts of social research, have brought forth new methods of general significance to the practice of statistics, in both theoretical and "applied" areas. These remarks should be taken as the impressions of someone who has tried to straddle the fence between statistics and social research throughout his career, not as a careful history of statistical ideas.

U.S. Government Contributions to Probability Sampling and Statistical Analysis

Abstract: The Federal Government of the United States has collected and published an increasing volume of statistics from the founding of the republic, but its contributions to statistical theory and method did not really begin until 1933. Before then, the bulk of Federal statistics was done by tabulation and compilation, and methods were largely intuitive. The Roosevelt New Deal and the Committee on Government Statistics and Information Services (COGSIS) made probability sampling and statistical analysis a significant part of Government planning and operations. By early in World War II, Federal statisticians had become leaders rather than just followers in statistical theory and methods. This article provides a summary of how this happened and especially of the subsequent development of survey sampling from finite populations. Attention is then turned to the development of statistical analysis in the Federal Government, a more diverse subject, which is both related to probability sampling in significant ways and very interesting because it is probably still in an early stage of development. This paper also provides commentary on some recent developments in the Federal statistical system in general during the period 1977 to 1992.

Women in Statistics in Academe: Mentors Matter

Abstract: Federal and state agencies, private industry and professional societies are developing programs to encourage women to enter the education "pipeline" for careers in science and technology. To reverse female students' underrepresentation in science and to retain incoming women in these fields, especially those entering academia, requires the active support of women and men faculty as mentors. The focus of the present manuscript addresses this issue. Here, we give a profile of women in statistics and, more broadly, in the sciences, and we outline the elements of a good mentor. Statistics are presented in support of our argument, but case studies form the basis for the recommendations.

R. A. Fisher and Evolutionary Theory

Abstract: R. A. Fisher, apart from his fundamental contributions to statistical science, fostered many developments of theoretical evolutionary science. In commemoration of Fisher's birth centenary (1991), this paper highlights several of Fisher's interests in evolutionary processes. These include the "Fundamental Theorem of Natural Selection," studies on the phenomenon of an even sex ratio in natural populations, the "runaway process" of sexual selection and models of polygenic inheritance. Some historical discussions and perspectives on evolutionary science and the Fisher legacy are also presented.

[Practical Markov Chain Monte Carlo]: Comment: Monitoring Convergence of the Gibbs Sampler: Further Experience with the Gibbs Stopper

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[Practical Markov Chain Monte Carlo]: Rejoinder: Replication without Contrition

Abstract: JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of content in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new forms of scholarship. For more information about JSTOR, please contact support@jstor.org. Institute of Mathematical Statistics is collaborating with JSTOR to digitize, preserve and extend access to Statistical Science. This article is from a volume of Statistical Science (1992; 7(4)) on the convergence of MCMC samples. The two main articles are: A complete list of the commentaries on these articles is shown on the next page.