This paper is a critique of the current direction of industrial statistics in the U.S. The sweep includes not just the toolkit of statistical methods most often employed in industry, but also international competitiveness, the corporate climate in which statistical solutions are sought and the educational process which trains applied statisticians. Much is found that is good, but bland endorsement does little to advance a field. Therefore most of the paper is deliberately iconoclastic. Almost all of the extreme viewpoints are rooted in the author's direct experience, working with statisticians and managers across a range of industries. Some of the perspective must be attributed to knowledgable gossip, from friends and students who are now employed by various companies. Incidentally, the paper reviews four new statistical textbooks for engineers and an edited volume of papers on experimental design for industry.

The English literature on gambling is examined from the early sixteenth to the mid-eighteenth centuries to try to discover the relationship between gambling and the development of the probability calculus. Throughout this entire time period, there is an overwhelming preoccupation in the literature with cheating at games of chance. The acts of cheating remain constant through time. However, the methods of cheating take various forms: for example false dice, legerdemain at cards and dice, perfect shuffles and card counting. Some probability calculations begin to creep into this literature near the end of the seventeenth century. What is demonstrated in this paper is that, contrary to the accepted folklore and even though there is some evidence that gamblers did have a concept of probability, gambling itself provided very little stimulus to the development of probability theory. In the other direction, the development of the probability calculus had a profound effect on gambling, namely in the formulation of a strategy of play. These strategies, first devised by Edmond Hoyle in the mid-eighteenth century and applied initially to the card game of whist, used very simple results in probability. As a result of this historical analysis, it is necessary to reanalyze the events surrounding the emergence of probability in the seventeenth century.

This paper reviews the early axiomatic treatments of quasi-linear means developed in the late 1920s and the 1930s. These years mark the beginning of both axiomatic and subjectivist probability theory as we know them today. At the same time, Kolmogorov, de Finetti and, in a sense, Ramsey took part in a perhaps lesser known debate concerning the notions of mean and certainty equivalent. The results they developed offer interesting perspectives on computing data summaries. They also anticipate key ideas in current normative theories of rational decision making. This paper includes an extended and self-contained introduction discussing the main concepts in an informal way. The remainder focusses primarily on two early characterizations of quasi-linear means: the Nagumo-Kolmogorov theorem and de Finetti's extension of it. These results are then related to Ramsey's expected utility theory, to von Neumann and Morgenstern's and to results on weighted means.

The three main points of this article are: 1. Quantum mechanical data differ from conventional data: for example, joint distributions usually cannot be defined conventionally; 2. rigorous methods have been developed for analyzing such data; the methods often use quantum-consistent analogs of classical statistical procedures; 3. with these procedures, statisticians, both data-analytic and more theoretically oriented, can become active participants in many new and emerging areas of science and biotechnology. In the physical realm described by quantum mechanics, many conventional statistical and probabilistic assumptions no longer hold. Probabilistic ideas are central to quantum theory but the standard Kolmogorov axioms are not uniformly applicable. Studying such phenomena requires an altered model for sample spaces, for random variables and for inference and decision making. The appropriate decision theory has been in development since the mid-1960s. It is both mathematically and statistically rigorous and conforms to the requirements of the known physical results. This article provides a tour of the structure and current applications of quantum-consistent statistical inference and decision theory. It presents examples, outlines the theory and considers applications and open problems. Certain central concepts of quantum theory are more clearly apprehended in terms of the quantum-consistent statistical decision theory. For example, the Heisenberg uncertainty principle can be obtained as a consequence of the quantum version of the Cramer-Rao inequality. This places concepts of statistical estimation and decision theory, and thus the statistician, at the center of the quantum measurement process. Quantum statistical inference offers considerable scope for participation by the statistical community, in both applications and foundational questions.