In animal breeding, Best Linear Unbiased Prediction, or BLUP, is a technique for estimating genetic merits. In general, it is a method of estimating random effects. It can be used to derive the Kalman filter, the method of Kriging used for ore reserve estimation, credibility theory used to work out insurance premiums, and Hoadley's quality measurement plan used to estimate a quality index. It can be used for removing noise from images and for small-area estimation. This paper presents the theory of BLUP, some examples of its application and its relevance to the foundations of statistics. Understanding of procedures for estimating random effects should help people to understand some complicated and controversial issues about fixed and random effects models and also help to bridge the apparent gulf between the Bayesian and Classical schools of thought.

Randomized clinical trials can present a scientific/ethical dilemma for clinical investigators. Statisticians have tended to focus on only one side of this dilemma, emphasizing the statistical and scientific advantages of randomized trials. Here we look at the other side, examining the personal care principle on which the physician-patient relationship is based and observing how that principle can make it difficult or impossible for a physician to participate in a randomized clinical study. We urge that the view that randomized clinical trials are the only scientifically valid means of resolving controversies about therapies is mistaken, and we suggest that a faulty statistical principle is partly to blame for this misconception. We conclude that statisticians should be more sensitive to the physician's responsibility to the individual patient and should, besides promoting randomized trials when they are ethically and practically feasible, work to improve the planning, execution, and analysis of nonrandomized clinical studies.

In the last quarter of the nineteenth century, three separate (but not entirely independent) papers appeared describing methods of studying complicated statistical procedures through the generation of random normal deviates. All three authors referred to problems in the smoothing of series as a motivation; all used different methods for generating the deviates. One presented itself as a method for general use and claimed to be suitable for efficient generation of large numbers of variates. The relevant works (by Erastus De Forest in 1876, by George H. Darwin in 1877, and by Francis Galton in 1890) are reproduced.

This paper is based on the 1989 Miller Memorial Lecture at Stanford University. The topic was chosen because of Rupert Miller's long involvement and significant contributions to multiple comparison procedures and theory. Our emphasis will be on the major questions that have received relatively little attention--on what one wants multiple comparisons to do, on why one wants to do that, and on how one can communicate the results. Very little attention will be given to how the results can be calculated--after all, there are books about that (e.g., Miller, 1966, 1981; Hochberg and Tamhane, 1987).