Causal inference is best understood using potential outcomes. This use is particularly important in more complex settings, that is, observational studies or randomized experiments with complications such as noncompliance. The topic of this lecture, the issue of estimating the causal effect of a treatment on a primary outcome that is “censored” by death, is another such complication. For example, suppose that we wish to estimate the effect of a new drug on Quality of Life (QOL) in a randomized experiment, where some of the patients die before the time designated for their QOL to be assessed. Another example with the same structure occurs with the evaluation of an educational program designed to increase final test scores, which are not defined for those who drop out of school before taking the test. A further application is to studies of the effect of job-training programs on wages, where wages are only defined for those who are employed. The analysis of examples like these is greatly clarified using potential outcomes to define causal effects, followed by principal stratification on the intermediated outcomes (e.g., survival).

Support vector machines (SVMs) appeared in the early nineties as optimal margin classifiers in the context of Vapnik’s statistical learning theory. Since then SVMs have been successfully applied to real-world data analysis problems, often providing improved results compared with other techniques. The SVMs operate within the framework of regularization theory by minimizing an empirical risk in a well-posed and consistent way. A clear advantage of the support vector approach is that sparse solutions to classification and regression problems are usually obtained: only a few samples are involved in the determination of the classification or regression functions. This fact facilitates the application of SVMs to problems that involve a large amount of data, such as text processing and bioinformatics tasks. This paper is intended as an introduction to SVMs and their applications, emphasizing their key features. In addition, some algorithmic extensions and illustrative real-world applications of SVMs are shown.

What role should assumptions play in inference? We present a small theoretical case study of a simple, clean case, namely the nonparametric comparison of two continuous distributions using (essentially) information about quartiles, that is, the central information displayed in a pair of boxplots. In particular, we contrast a suggestion of John Tukey—that the validity of inferences should not depend on assumptions, but assumptions have a role in efficiency—with a competing suggestion that is an aspect of Hansen’s generalized method of moments—that methods should achieve maximum asymptotic efficiency with fewer assumptions. In our case study, the practical performance of these two suggestions is strikingly different. An aspect of this comparison concerns the unification or separation of the tasks of estimation assuming a model and testing the fit of that model. We also look at a method (MERT) that aims not at best performance, but rather at achieving reasonable performance across a set of plausible models.

Generalized linear models (GLMs) have been used quite effectively in the modeling of a mean response under nonstandard conditions, where discrete as well as continuous data distributions can be accommodated. The choice of design for a GLM is a very important task in the development and building of an adequate model. However, one major problem that handicaps the construction of a GLM design is its dependence on the unknown parameters of the fitted model. Several approaches have been proposed in the past 25 years to solve this problem. These approaches, however, have provided only partial solutions that apply in only some special cases, and the problem, in general, remains largely unresolved. The purpose of this article is to focus attention on the aforementioned dependence problem. We provide a survey of various existing techniques dealing with the dependence problem. This survey includes discussions concerning locally optimal designs, sequential designs, Bayesian designs and the quantile dispersion graph approach for comparing designs for GLMs.

In 1693, Isaac Newton answered a query from Samuel Pepys about a problem involving dice. Newton’s analysis is discussed and attention is drawn to an error he made.

Ulf Grenander was born in Vastervik, Sweden, on July 23, 1923. He started his undergraduate education at Uppsala University, and earned his B.A. degree in 1946, the Fil. Lic. degree in 1948 and the Fil. Dr. degree in 1950, all from the University of Stockholm. His Ph.D. thesis advisor was Harald Cramér. Professor Grenander is well known for pathbreaking research in a number of areas including pattern theory, computer vision, inference in stochastic processes, probabilities on algebraic structures and actuarial mathematics. He has published more than one dozen influential books, of which Statistical Analysis of Stationary Time Series (1957, coauthored with M. Rosenblatt), Probabilities on Algebraic Structures (1963; also in Russian) and Abstract Inference (1981b) are regarded as classics. His three-volume lecture notes, namely, Pattern Synthesis (vol. I, 1976), Pattern Analysis (vol. II, 1978) and Regular Structures (vol. III, 1981a; also in Russian) created and nurtured a brand new area of research. During 1951–1966, Professor Grenander’s career path took him to the University of Chicago (1951–1952), the University of California–Berkeley (1952–1953), the University of Stockholm (1953–1957), Brown University (1957–1958) and the Institute for Insurance Mathematics and Mathematical Statistics (1958–1966) as its Professor and Director. From 1966 until his retirement he was L. Herbert Ballou University Professor at Brown University. Professor Grenander also held the position of Scientific Director (1971–1973) of the Swedish Institute of Applied Mathematics. He has earned many honors and awards, including Arhennius Fellow (1948), Fellow of the Institute of Mathematical Statistics (1953), Prize of the Nordic Actuaries (1961), Arnberger Prize of the Royal Swedish Academy of Science (1962), Member of the Royal Swedish Academy of Science (1965), Guggenheim Fellowship (1979) and Honorary Fellow of the Royal Statistical Society, London (1989). He has delivered numerous prestigious lectures, including the Rietz Lecture (1985), the Wald Lectures (1995) and the Mahalanobis Lecture (2004). Professor Grenander received an Honorary D.Sc. degree (1993) from the University of Chicago and is a Fellow of both the American Academy of Arts and Sciences (1995) and the National Academy of Sciences, U.S.A. (1998). Professor Grenander’s career, life, passion and hobbies can all be summarized by one simple word: Mathematics.