Survival analysis as used in the medical context is focused on the concepts of survival function and hazard rate, the latter of these being the basis both for the Cox regression model and of the counting process approach. In spite of apparent simplicity, hazard rate is really an elusive concept, especially when one tries to interpret its shape considered as a function of time. It is then helpful to consider the hazard rate from a different point of view than what is common, and we will here consider survival times modeled as first passage times in stochastic processes. The concept of quasistationary distribution,which is a well-defined entity for various Markov processes, will turn out to be useful.

We study these matters for a number of Markov processes, including the following: finite Markov chains; birth-death processes; Wiener processes with and without randomization of parameters; and general diffusion processes. An example of regression of survival data with a mixed inverse Gaussian distribution is presented.

The idea of viewing survival times as first passage times has been much studied by Whitmore and others in the context of Wiener processes and inverse Gaussian distributions. These ideas have been in the background compared to more popular appoaches to survival data, at least within the field of biostatistics,but deserve more attention.

In 1924 Yule observed that distributions of number of species per genus were typically long­tailed, and proposed a stochastic model to fit these data. Modern taxonomists often prefer to represent relationships between species via phylogenetic trees; the counterpart to Yule’s observation is that actual reconstructed trees look surprisingly unbalanced. The imbalance can readily be seen via a scatter diagram of the sizes of clades involved in the splits of published large phylogenetic trees. Attempting stochastic modeling leads to two puzzles. First, two somewhat opposite possible biological descriptions of what dominates the macroevolutionary process (adaptive radiation; “neutral” evolution) lead to exactly the same mathematical model (Markov or Yule or coalescent). Second, neither this nor any other simple stochastic model predicts the observed pattern of imbalance. This essay represents a probabilist’s musings on these puzzles, complementing the more detailed survey of biological literature by Mooers and Heard, Quart. Rev. Biol. 72 [(1997) 31–54].

Prosecuting those arrested for the unlawful possession, distribution or importation of illicit drugs, such as powder cocaine, crack cocaine, heroin and LSD, is usually both time­consuming and expensive, primarily because of the need to determine “beyond a reasonable doubt” the total amount of drugs seized in each case. Accuracy is important since penalties (imprisonment or fines) depend upon the quantity seized. Substantial backlogs in processing drug cases often develop as a result. In some jurisdictions, complete testing and analysis of all substances seized froma defendant are customary in support of a case, while in other jurisdictions randomsampling of drugs and the subsequent presentation of an estimate of the total amount seized have been used for many years. Due to pressure from crime laboratories and prosecutors, who point to major increases in their caseloads as well as a trend toward decreasing funding and staffing for the crime laboratories, jurisdictions which currently carry out a complete census of all seized evidence are now seriously considering a change in their methodology with a view to instituting new guidelines for the scientific sampling of evidence. In this article, we discuss the statistical and legal issues that have arisen in cases involving illicit drugs.

Masqueraders in computer intrusion detection are people who use somebody else’s computer account. We investigate a number of statistical approaches for detecting masqueraders. To evaluate them, we collected UNIX command data from 50 users and then contaminated the data with masqueraders. The experiment was blinded. We show results from six methods, including two approaches from the computer science community.

Ralph A. Bradley was born in Smith Falls, Ontario, Canada on Nvember 28, 1923, but grew up in the village of Wellington on the shores of Lake Ontario. He graduated from Queen’s University in 1944 with an honors degree in mathematics and physics, was in the Canadian Army, 1944–1945 and returned to Queen's to complete an M.A. degree in 1946. In 1946 he entered the then new doctoral program in theoretical statistics at the University of Nrth Carolina and received the Ph.D. degree in June, 1949. His first academic position was at McGill University, 1949–1950, followed by nine years at the Virginia Polytechnic Institute, 1950–1958. Bradley moved to Florida State University in 1959 to found a Department of Statistics there, heading the department until 1978, with the exception of ten months in Egypt in 1966 as a consultant to the Ford Foundation and the Institute of Statistical Studies and Research of the University of Cairo. He moved to the University of Georgia as Research Professor of Statistics in 1982. Although he retired in 1992, he continues to participate in activities in statistics there. He has been named Professor Emeritus at both Florida State and Georgia Universities.

Bradley has played a leadership role in the professional societies. He was Editor of Biometrics, 1957–1962, and Vice­President and President of the Eastern North American Region (1963–1965). He served as Vice­President (1975–1978) and President (1981) of the American Statistical Association (ASA). He headed (with Margaret E. Martin) the Coordinating Committee of the ASA Building and Development Fund (1982–1988) and was a member of the Future Goals Committee (1980). He has also served on various committees of the Institute of Mathematical Statistics, been active in the International Statistical Institute, the Gordon Research Conferences, the Southern Regional Committee on Statistics, and the Ntional Institute of Statistical Sciences. He has served on the editorial boards of Biometrics, the Journal of Statistical Computing and Simulation, and Communications in Statistics­Theory and Methods and acted as an editorial advisor on the Wiley Series on Probability and Statistics (1954--1998).

Bradley has been active in research throughout his career. He has over 110 research papers in such areas as design of experiments, non­ parametric statistics, methodology for sensory evaluations, sequential analysis, multivariate analysis, probability theory and computing tech­ niques. Most of his papers stemmed from his statistical consulting on applied problems, or from the need to develop new theory to solve such problems. Bradley's consulting with General Foods on statistical methods in product evaluation was particularly influential in stimulating his own research and the research of others.