Setting confidence bounds is an essential part of the reporting of experimental results. Current physics experiments are often done to measure nonnegative parameters that are small and may be zero and to search for small signals in the presence of backgrounds. These are examples of experiments which offer the possibility of yielding a result, recognized a priori to be relatively improbable, of a negative estimate for a quantity known to be positive. The classical Neyman procedure for setting confidence bounds in this situation is arguably unsatisfactory and several alternatives have been recently proposed. We compare methods for setting Gaussian and Poisson confidence intervals for cases in which the parameter to be estimated is bounded. These procedures lead to substantially different intervals when a relatively improbable observation implies a parameter estimate beyond the bound.

As decision- and policy-makers come to rely increasingly on estimates and simulations produced by computerized models of the world, in areas as diverse as climate prediction, transportation planning, economic policy and civil engineering, the need for objective evaluation of the accuracy and utility of such models likewise becomes more urgent. This article summarizes a two-day workshop that took place in Santa Fe, New Mexico in December 1999, whose focus was the evaluation of complex computer models. Approximately half of the workshop was taken up with formal presentation of four computer models by their creators, each paired with an initial assessment by a statistician. These prepared papers are presented, in shortened form, in Section 3 of this paper. The remainder of the workshop was devoted to introductory and summary comments, short contributed descriptions of related models and a great deal of floor discussion, which was recorded by assigned rapporteurs. These are presented in Sections 2 and 4 in the paper. In the introductory and concluding sections we attempt to summarize the progress made by the workshop and suggest next steps.

Sample size determination (SSD) is a crucial aspect of experimental design. Two SSD problems are considered here. The first concerns how to select a sample size to achieve specified performance with regard to one or more features of a model. Adopting a Bayesian perspective, we move the Bayesian SSD problem from the rather elementary models addressed in the literature to date in the direction of the wide range of hierarchical models which dominate the current Bayesian landscape. Our approach is generic and thus, in principle, broadly applicable. However, it requires full model specification and computationally intensive simulation, perhaps limiting it practically to simple instances of such models. Still, insight from such cases is of useful design value. In addition, we present some theoretical tools for studying performance as a function of sample size, with a variety of illustrative results. Such results provide guidance with regard to what is achievable. We also offer two examples, a survival model with censoring and a logistic regression model.

The second problem concerns how to select a sample size to achieve specified separation of two models. We approach this problem by adopting a screening criterion which in turn forms a model choice criterion. This criterion is set up to choose model 1 when the value is large, model 2 when the value is small. The SSD problem then requires choosing $n_{1}$ to make the probability of selecting model 1 when model 1 is true sufficiently large and choosing $n_{2}$ to make the probability of selecting model 2 when model 2 is true sufficiently large. The required n is $\max(n_{1}, n_{2})$. Here, we again provide two illustrations. One considers separating normal errors from t errors, the other separating a common growth curve model from a model with individual growth curves.

This paper is addressed to engineers and statisticians working on topics in reliability and survival analysis. It is also addressed to designers of network systems. The material here is prompted by problems of infrastructure assurance and protection. Infrastructure systems, like the internet and the power grid, comprise a web of interconnected components experiencing interacting (or dependent) failures. Such systems are prone to a paralyzing collapse caused by a succession of rapid failures; this phenomenon is referred to as "cascading failures." Assessing the reliability of an infrastructure system is a key step in its design. The purpose of this paper is to articulate on aspects of infrastructure reliability, in particular the notions of chance, interaction, cause and cascading.

Following a commentary on how the term "reliability" is sometimes interpreted, the paper begins by making the argument that exchangeability is a meaningful setting for discussing interaction. We start by considering individual components and describe what it means to say that they are exchangeable. We then show how exchangeability leads us to distinguish between chance and probability. We then look at how entire networks can be exchangeable and how components within a network can be dependent. The above material, though expository, serves the useful purpose of enabling us to introduce and make precise the notions of causal and cascading failures. Classifying dependent failures as being either causal or cascading and characterizing these notions is a contribution of this paper. The others are a focus on networks and their setting in the context of exchangeability.

A simple model for cascading failures closes the paper. A virtue of this model is that it enables us to make the important claim that causal failures are more deleterious to infrastructure reliability than cascading failures. This claim, being contrary to a commonly held perception of network designers and operators, is perhaps the key contribution of this paper.

Samuel Kotz was born in Harbin, China, on August 28, 1930. After graduating with honors in 1946 from the Russian School in Harbin, he studied electrical engineering at Harbin Institute of Technology during 1947-1949. In 1949 he emigrated to Israel, where, after two years of military service, he studied at the Hebrew University in Jerusalem, obtaining an M.A. with honors in Mathematics in 1956. Following two years at the Israeli Meteorological Service, he entered graduate school at Cornell University and obtained a Ph.D. degree in Mathematics in 1960. After research positions at the University of North Carolina, Chapel Hill, and the University of Toronto, he joined the latter institution as an Associate Professor in 1964. He moved to Temple University, Philadelphia, in 1967 as Professor of Mathematics and then to the University of Maryland, College Park, in 1979 as Professor in the College of Business and Management. He took early retirement and moved to George Washington University in 1997.

Samuel Kotz has made substantial contributions in several areas of statistics--including systems of distributions, measures of dependence, multivariate analysis, characterizations, limit distributions, replacement theory, quality control, information theory and applications of statistics. He is the senior coeditor-in-chief of the thirteen-volume Encyclopedia of Statistical Sciences, an author or coauthor of over one hundred and fifty articles on statistical methodology and theory, twelve books in the field of statistics and quality control and three Russian-English scientific dictionaries and coauthor of the often-cited compendium of statistical distributions. His efforts, excellence and contributions were recognized by the award of honorary Doctor of Science degrees from Harbin Institute of Technology (China) in 1988, from the University of Athens (Greece) in 1995 and from Bowling Green State University (Ohio, U.S.A.) in 1997. In 1997 a volume containing thirty-eight essays was published in honor of his sixty-fifth birthday. He was awarded membership in the Washington Academy of Sciences in 1998. He is a Fellow of the Royal Statistical Society, Fellow of the American Statistical Association, Fellow of the Institute of Mathematical Statistics and an elected member of the International Statistical Institute.