Showing papers in "Statistical Science in 1999"

Bayesian Model Averaging: A Tutorial

Abstract: Standard statistical practice ignores model uncertainty. Data analysts typically select a model from some class of models and then proceed as if the selected model had generated the data. This approach ignores the uncertainty in model selection, leading to over-confident inferences and decisions that are more risky than one thinks they are. Bayesian model averaging (BMA)provides a coherent mechanism for accounting for this model uncertainty. Several methods for implementing BMA have recently emerged. We discuss these methods and present a number of examples.In these examples, BMA provides improved out-of-sample predictive performance. We also provide a catalogue of currently available BMA software.

Confounding and Collapsibility in Causal Inference

Abstract: Consideration of confounding is fundamental to the design and analysis of studies of causal effects. Yet, apart from confounding in experimental designs, the topic is given little or no discussion in most statistics texts. We here provide an overview of confounding and related concepts based on a counterfactual model for causation. Special attention is given to definitions of confounding, problems in control of confound- ing, the relation of confounding to exchangeability and collapsibility, and the importance of distinguishing confounding from noncollapsibility.

Estimating Animal Abundance: Review III

Abstract: The literature describing methods for estimating animal abundance and related parameters continues to grow. This paper reviews recent developments in the subject over the past seven years and updates two previous reviews.

Integrated likelihood methods for eliminating nuisance parameters

Abstract: Elimination of nuisance parameters is a central problem in statistical inference and has been formally studied in virtually all approaches to inference. Perhaps the least studied approach is elimination of nuisance parameters through integration, in the sense that this is viewed as an almost incidental byproduct of Bayesian analysis and is hence not something which is deemed to require separate study. There is, however, considerable value in considering integrated likelihood on its own, especially versions arising from default or noninformative priors. In this paper, we review such common integrated likelihoods and discuss their strengths and weaknesses relative to other methods.

Parrondo's paradox

Abstract: We introduce Parrondo's paradox that involves games of chance. We consider two fair gambling games, A and B, both of which can be made to have a losing expectation by changing a biasing parameter $\epsilon$. When the two games are played in any alternating order, a winning expectation is produced, even though A and B are now losing games when played individually. This strikingly counter­intuitive result is a consequence of discrete­time Markov chains and we develop a heuristic explanation of the phenomenon in terms of a Brownian ratchet model. As well as having possible applications in electronic signal processing, we suggest important applications in a wide range of physical processes, biological models, genetic models and sociological models. Its impact on stock market models is also an interesting open question.

From association to causation: some remarks on the history of statistics

Abstract: The "numerical method" in medicine goes back to Pierre Louis' 1835 study of pneumonia and John Snow's 1855 book on the epi- demiology of cholera. Snow took advantage of natural experiments and used convergent lines of evidence to demonstrate that cholera is a wa- terborne infectious disease. More recently, investigators in the social and life sciences have used statistical models and significance tests to deduce cause-and-effect relationships from patterns of association; an early ex- ample is Yule's 1899 study on the causes of poverty. In my view, this modeling enterprise has not been successful. Investigators tend to ne- glect the difficulties in establishing causal relations, and the mathemat- ical complexities obscure rather than clarify the assumptions on which the analysis is based. Formal statistical inference is, by its nature, conditional. If maintained hypotheses A, B, C,... hold, then H can be tested against the data. How- ever, if A, B, C, . . . remain in doubt, so must inferences about H. Careful scrutiny of maintained hypotheses should therefore be a critical part of empirical work-a principle honored more often in the breach than the observance. Snow's work on cholera will be contrasted with modern studies that depend on statistical models and tests of significance. The examples may help to clarify the limits of current statistical techniques for making causal inferences from patterns of association.

Choice as an Alternative to Control in Observational Studies

Abstract: In a randomized experiment, the investigator creates a clear and relatively unambiguous comparison of treatment groups by exerting tight control over the assignment of treatments to experimental subjects, ensuring that comparable subjects receive alternative treatments. In an observational study, the investigator lacks control of treatment assignments and must seek a clear comparison in other ways. Care in the choice of circumstances in which the study is conducted can greatly influence the quality of the evidence about treatment effects. This is illustrated in detail using three observational studies that use choice effectively, one each from economics, clinical psychology and epidemiology. Other studies are discussed more briefly to illustrate specific points. The design choices include (i) the choice of research hypothesis, (ii) the choice of treated and control groups, (iii) the explicit use of competing theories, rather than merely null and alternative hypotheses, (iv) the use of internal replication in the form of multiple manipulations of a single dose of treatment, (v) the use of undelivered doses in control groups, (vi) design choices to minimize the need for stability analyses, (vii) the duration of treatment and (viii) the use of natural blocks.

The Emperor’s new tests

Abstract: In the past two decades, striking examples of allegedly infe- rior likelihood ratio tests (LRT) have appeared in the statistical litera- ture. These examples, which arise in multiparameter hypothesis testing problems, have several common features. In each case the null hypothe- sis is composite, the size a LRT is not similar and hence biased, and competing size a tests can be constructed that are less biased, or even unbiased, and that dominate the LRT in the sense of being everywhere more powerful. It is therefore asserted that in these examples and, by implication, many other testing problems, the LR criterion produces "inferior," "deficient," "undesirable," or "flawed" statistical procedures. This message, which appears to be proliferating, is wrong. In each example it is the allegedly superior test that is flawed, not the LRT. At worst, the "superior" tests provide unwarranted and inappropriate in- ferences and have been deemed scientifically unacceptable by applied statisticians. This reinforces the well-documented but oft-neglected fact that the Neyman-Pearson theory desideratum of a more (or most) powerful size a test may be scientifically inappropriate; the same is true for the criteria of unbiasedness and a-admissibility. Although the LR criterion is not infallible, we believe that it remains a generally reasonable first option for non-Bayesian parametric hypothesis-testing problems.

On the history of maximum likelihood in relation to inverse probability and least squares

Abstract: It is shown that the method of maximum likelihood occurs in rudimentary forms before Fisher [Messenger of Mathematics 41 (1912) 155–160], but not under this name. Some of the estimates called “most probable” would today have been called “most likely.” Gauss [Z. Astronom. Verwandte Wiss. 1 (1816) 185–196] used invariance under parameter transformation when deriving his estimate of the standard deviation in the normal case. Hagen [Grundzuge der Wahrschein­lichkeits­Rechnung, Dummler, Berlin (1837)] used the maximum likelihood argument for deriving the frequentist version of the method of least squares for the linear normal model. Edgeworth [J. Roy. Statist. Soc. 72 (1909) 81–90] proved the asymptotic normality and optimality of the maximum likelihood estimate for a restricted class of distributions. Fisher had two aversions: noninvariance and unbiasedness. Replacing the posterior mode by the maximum likelihood estimate he achieved invariance, and using a two­stage method of maximum likelihood he avoided appealing to unbiasedness for the linear normal model.

Analysis of Local Decisions Using Hierarchical Modeling, Applied to Home Radon Measurement and Remediation

Abstract: This paper examines the decision problems associated with measurement and remediation of environmental hazards, using the example of indoor radon (a carcinogen) as a case study. Innovative methods developed here include (1) the use of results from a previous hierarchical statistical analysis to obtain probability distributions with local variation in both predictions and uncertainties, (2) graphical methods to display the aggregate consequences of decisions by individuals and (3) alternative parameterizations for individual variation in the dollar value of a given reduction in risk. We perform cost­benefit analyses for a variety of decision strategies, as a function of home types and geography, so that measurement and remediation can be recommended where it is most effective. We also briefly discuss the sensitivity of policy recommendations and outcomes to uncertainty in inputs. For the home radon example, we estimate that if the recommended decision rule were applied to all houses in the United States, it would be possible to save the same number of lives as with the current official recommendations for about 40% less cost.

Analyzing Musical Structure and Performance : A Statistical Approach

Abstract: Musical performance theory and the theory of musical structure in general is a rapidly developing field of musicology that has wide practical implications. Due to the complex nature of music, statistics is likely to play an important role. In spite of this, up to the present, applications of statistical methods to music have been rare and mostly limited to a formal confirmation of results obtained by other methods. The present paper introduces a statistical approach to the analysis of metric, melodic and harmonic structures of a score and their influence on musical performance. Examples by Schumann, Webern and Bach illustrate the proposed method of numerical encoding and hierarchical decomposition of score information. Application to performance data is exemplified by the analysis of tempo data for Schumann's “Traumerei” op. 15/7. The paper demonstrates why statistics should play a major active part in performance research. The results obtained here are only a starting point and should, hopefully, stimulate a fruitful discussion between statisticians, musicologists, computer scientists and other researchers interested in the area.

Solving the Bible Code Puzzle

Abstract: A paper of Witztum, Rips and Rosenberg in this journal in 1994 made the extraordinary claim that the Hebrew text of the Book of Genesis encodes events which did not occur until millennia after the text was written. In reply, we argue that Witztum, Rips and Rosenberg's case is fatally defective, indeed that their result merely reflects on the choices made in designing their experiment and collecting the data for it. We present extensive evidence in support of that conclusion. We also report on many new experiments of our own, all of which failed to detect the alleged phenomenon.

“Student” and small-sample theory

Abstract: The paper discusses the contributions Student (W. S. Gosset) made to the three stages in which small-sample methodology was established in the period 1908-1933: (i) the distributions of the test- statistics under the assumption of normality, (ii) the robustness of these distributions against nonnormality, (iii) the optimal choice of test statistics. The conclusions are based on a careful reading of the correspondence of Gosset with Fisher and E. S. Pearson.

Gustav Elfving's Impact on Experimental Design

Abstract: During my visit at Stanford University in the summer and fall of 1951, some problems proposed by the National Security Agency (NSA) for an Office of Naval Research (ONR) applied research grant led to two of my publications [1, 2] which had a profound effect on my future research. Both papers had relevance to issues in experimental design. One of these concerned optimal design for estimation. Among other results, it demonstrated that, asymptotically, locally optimal designs for estimating one parameter require the use of no more than k of the available experiments, when the distribution of the data from these experiments involves k unknown parameters. A trivial example would be that to estimate the slope of a straight line regression with constant variance, where the explanatory variable x is confined to the interval [-1, 1], an optimal design requires observations concentrated at the two ends, x = 1 and x = -1. Shortly after I derived this result, I discovered a related publication by Gustav Elfving [3]. While Elfving's result is restricted to k-dimensional regression experiments, it gives an elegant geometrical representation of the optimal design accompanied by an equally elegant derivation, which I still find pleasure in presenting to audiences who are less acquainted with this paper than they should be. In some problems, practical considerations make it impossible to apply optimal designs. One beauty of the Elfving result is that the graphical representation of his result makes it rather clear how much is lost by applying some restricted suboptimal methods, and gives some guidance to wise compromises between optimality and practicality. By 1950, experimental design was a wellestablished field of statistics. Major sources of application were in agriculture and chemistry, and

Gustav Elfving's contribution to the emergence of the optimal experimental design theory

Abstract: Gustav Elfving contributed to the genesis of optimal experimental design theory with several papers mainly in the 1950s These papers are presented and briefly analyzed The connections between Elfving’s results and the results of his successors are elucidated to stress the relevance of Elfving’s impact on the development of optimal design theory

A conversation with Lucien Le Cam

Abstract: Lucien Le Cam is currently Emeritus Professor of Mathematics and Statistics at the University of California, Berkeley. He was born on November 18, 1924, in Croze, Creuse, France. He received a Licence es Sciences from the University of Paris in 1945, and a Ph.D. in Statistics from the University of California at Berkeley in 1952. He has been on the faculty of the Statistics Department at Berkeley since 1952 except for a year in Montreal, Canada, as the Director of the Centre de Recherches Mathematiques (1972--1973). He served as Chairman of the Department of Statistics at Berkeley (1961–1965) and was co­editor with J. Neyman of the Berkeley Symposia. Professor Le Cam is the principal architect of the modern asymptotic theory of statistics and has also made numerous other contributions. He developed a mathematical system that substantially extended Wald's statistical decision theory to the version being used today. With his introduction of the distance between experiments, we now have a coherent statistical theory that links the asymptotics and the statistical decision theory. Encompassed in the theory are the concepts of contiguity, asymptotic sufficiency, a new method of constructing estimators (the one­step estimator), the theory of local asymptotic normality (LAN), metric dimension and numerous other seminal ideas. The metric dimension, introduced in 1973, has been found to be fundamentally important in studying nonparametric or semiparametric problems. This monumental work culminated in a big book, Asymptotic Methods in Statistical Decision Theory, published by Springer in 1986. Professor Le Cam's scientific contributions are not limited to theoretical statistics. At age 23 he introduced the characteristic functional technique (after Kolmogorov, but independently) to study the spatial and temporal distribution of rainfall and its relation to stream flow. It resulted in a model known as Le Cam’s model in hydrology. In the domain of probability theory, he was one of the early contributors to the study of convergence of measures in topological spaces. He refined the approximation theorems and the concentration inequalities of Kolmogorov and made extensions of these results to infinite­dimensional spaces. We also owe to him the introduction of the concepts of $\tau$-smooth, and $\sigma$­smooth that are widely used today. In honor of his 70th birthday in 1994, a week­long workshop and a conference were held at Yale University, organized by Professor David Pollard. In addition, a Festschrift for Le Cam, Research Papers in Probability and Statistics Papers, was published by Springer in 1997. He is married to Louise Romig, the daughter of a founder of statistical quality control, Harry Romig. They have three grown children, Denis, Steven and Linda.

The life and work of Gustav Elfving

Abstract: This article outlines the scientific work and life of the Finnish statistician, probabilist, and mathematician Gustav Elfving (1908–1984). Elfving’s academic career, scientific contacts, and personal life are sketched, and his main research contributions to the fields of statistics, probability, and mathematics are reviewed. (Elfving’s pioneering work in optimal design of experiments is not covered, as this topic will be treated elsewhere in this issue.) A chronological bibliography of Gustav Elfving is also given.

A history of the Statistical Society of Canada: the formative years (with discussion)

Abstract: The year 1997 marked the twenty­fifth anniversary of the foundation of the first Canadian statistical association and the silver jubilee of The Canadian Journal of Statistics (CJS). This paper relates the events and circumstances that led to the creation of these institutions. It also describes how frictions between individuals, as well as diverging regional and professional interests, soon led to the rise of a second, rival association that eventually merged with the first in 1977–78 to form what is now known as the Statistical Society of Canada (SSC). This historical account is based on abundant archival material and on interviews conducted by the authors in preparation for a commemorative presentation they made at the Annual Meeting of the SSC, June 2, 1997, in Fredericton, New Brunswick.

A conversation with Chin Long Chiang

Abstract: Chin Long Chiang, Professor in the Graduate School, Univer- sity of California, Berkeley, was born on November 12,1914, in Ningbo, Zhejiang Province, China. He received his B.A.degree in economics in 1940 from National Tsing Hua University in China; his M.A.degree in 1948 and his Ph.D. degree in 1953, both in statistics from University of California, Berkeley.Dr.Chiang was on the U. C. Berkeley faculty for 36 years and has served as Chairman of the Program in Biostatistics, of the Division of Measurement Sciences and of the Faculty of the School of Public Health,and as Co-chairman of the Group of Biostatistics. When he retired in l987, the University honored him with “The Berkeley Citation ” award for his “distinguished achievement.” He was recalled to active duty in 1996. Dr.Chiang has been invited as a visiting professor at the following universities: Harvard; Yale; Pittsburgh; North Carolina; Emory; Michigan; Minnesota; Texas; Vanderbilt; and Washington at Seattle. He has given courses at Peking University, Beijing Medical University and Tongji Medical University, all in China, and at Tunghai University in Taiwan. In addition to his many scientific articles, he has published four books, two of which are about stochastic processes. Three of his books have been translated into Chinese and one into Japanese. Professor Chiang is a Fellow of the American Statistical Association, of the Institute of Mathematical Statistics and of the Royal Statistical Society of London. He has served as a special consultant to several national and international agencies. Professor Chiang is residing with his wife in Berkeley, California. They have two sons and one daughter, and two grandsons.

A conversation with I. Richard Savage (with the assistance of Bruce Spencer)

Abstract: I. Richard Savage was born in Detroit on October 26, 1925. He attended Northern High School in Detroit and received a bachelor's degree in mathematics at the University of Chicago when he was nineteen. Subsequently, he received a master's degree in mathematics from the University of Michigan (1945) and a Ph.D. in mathematical statistics from Columbia in 1953. While at Columbia, he met JoAnn Osherow and they were married in 1950. They have two daughters, Martha, born in 1951, and Donna, born in 1953. His career began with a three­year (1951–1954) stint as a mathematical statistician in the National Bureau of Standards, followed by a three­ year visiting appointment in the Department of Statistics at Stanford University. From 1957 to 1963, Savage was a professor of Statistics, Biostatistics and Economics at the University of Minnesota. He then spent the next eleven years on the faculty of Florida State University in the Department of Statistics. From 1974 until his retirement in 1990, he was a professor in the Department of Statistics at Yale University. His research interests include rank order statistics, statistics and pub­ lic policy and Bayesian statistics. He served as Coeditor of the Journal of the American Statistical Association (1968, as Editor of the Annals of Statistics (1974–1977), and as President of the American Statistical Association (1984). Because of his commitment to advance proper use of statistics to shape public policy, he has been heavily involved with the Committee on National Statistics of the National Research Council. The book Statistics and Public Policy, edited by Bruce Spencer, was published in 1997 in honor of Savage's contributions to statistics.

A conversation with Lincoln E. Moses

Abstract: Lincoln E. Moses was born on December 21, 1921 in Kansas City, Missouri. He attended San Bernardino Valley Junior College from 1937 to 1939 and earned an AA degree, earned an A.B. in Social Sciences from Stanford University in 1941 and a Ph.D. in Statistics from Stanford University in 1950. He was Assistant Professor of Education at Teacher’s College, Columbia University (1950–1952), Assistant Professor of Statistics in the Department of Statistics and the Department of Preventive Medicine, Stanford University (1952–1955), Associate professor in those departments from 1955 to 1959, and Professor of Statistics in the Department of Statistics and the Department of Research and Health Policy, Stanford University from 1959 until his retirement in 1992. He is now Professor Emeritus. He was Executive Head of the Department of Statis­ tics at Stanford from 1964 to 1968. He served as Associate Dean, Humanities and Sciences, Stanford University (1965–1968 and 1985–1986) and Dean of Graduate Studies, Stanford University, 1969–1975. He was Administrator, Energy Information Administration, Department of Energy, 1978–1980 after being appointed by President Carter in 1977. His many recognitions and honors include being Fellow, John Simon Guggenheim Memorial Foundation, 1960–1961, L. L. Thurstone Distinguished Fellow, University of North Carolina, 1968–1969, Fellow, Center for Advanced Study in the Behavioral Sciences, 1975–1976. He is a Fellow of the Institute of Mathematical Statistics, a Fellow of the American Statistical Association, an elected member of the International Statistical Institute, a Fellow of the American Association for the Advancement of Science, a Fellow of the American Academy of Arts and Sciences, a member of Phi Beta Kappa and a member of the Institute of Medicine. In 1980 he received the Distinguished Service Medal of the U.S. Department of Energy.