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This article surveys the evolution of stock market trading over a 60-year period. It begins before 1960, when there was no database widely available to conduct a statistical analysis of stock price movements. This changed in the 1960s with the introduction of the Center for Research in Security Prices database. A major finding was the heavy-tailed nature of stock returns. The 1960s also brought major theoretical developments, including the martingale theory of stock price processes and the efficient market hypothesis. This hypothesis prevailed until the 1990s, when the discovery of market anomalies led to statistical arbitrage strategies. We describe the use of modern machine learning methods, such as AdaBoost and random forests, which can combine some of these strategies into an improved trading strategy. The twenty-first century was marked by the rapid evolution of electronic markets and the rise of computer-driven high-frequency trading based on computing technology, low latency access, and limit order book modeling.

Evaluations of the costs and benefits of US drinking water standards typically consider only a single contaminant or class of contaminants. However, the US Environmental Protection Agency (USEPA) is in the process of formulating and implementing multiple new regulations, and drinking water systems will be expected to comply with all of them simultaneously. The joint effects of different regulations are not necessarily the sum of the effects of the individual regulations. In some cases, treating for one contaminant may remove other contaminants. In other instances, treating for one contaminant (e.g., pathogens) may make it more difficult to comply with regulations for other contaminants (e.g., disinfection byproducts). A simulation model was developed to assess the national costs and benefits of compliance with multiple drinking water standards. For each of the approximately 55,000 US community water systems, concentrations of raw water constituents, treatment type, and removal efficiencies were sampled from statistical models and used to compute finished water concentrations. Modeling the effects of different regulations at the same time and using the same modeling assumptions allowed the cost‐effectiveness of alternative regulations to be compared on an equal basis. For example, this study found that the revised arsenic maximum contaminant level (MCL) is more cost‐effective than the uranium MCL at reducing cancer risk. By facilitating more direct comparison of the cost‐effectiveness of different regulations, an integrated model can help utilities prioritize their regulatory options. In addition, a better understanding of the joint effects of different regulations may help USEPA and other stakeholders to design more effective overall regulatory programs.

For Savage (1954) as for de Finetti (1974), the existence of subjective (personal) probability is a consequence of the normative theory of preference. (De Finetti achieves the reduction of belief to desire with his generalized Dutch-Book argument for Previsions.) Both Savage and de Finetti rebel against legislating countable additivity for subjective probability. They require merely that probability be finitely additive. Simultaneously, they insist that their theories of preference are weak, accommodating all but self-defeating desires. In this paper we dispute these claims by showing that the following three cannot simultaneously hold: (i) Coherent belief is reducible to rational preference, i.e. the generalized Dutch-Book argument fixes standards of coherence. (ii) Finitely additive probability is coherent. (iii) Admissible preference structures may be free of consequences, i.e. they may lack prizes whose values are robust against all contingencies.

In the case that vectors X and Y have a joint multivariate normal distribution, tolerance regions are found for the best linear predictor of Y using X if samples are used to estimate the regression coeffierante. Tolerance regions are also found for Y. In addition, simultaneous tolerance intervals for all linear functions of Y or of the best linear predictor of Y using X are found.

A programme for fostering the growth of victims and potential victims of child abuse is evaluated via a longitudinal and cross‐sectional study. A Bayesian analysis of the data is presented. Some linear hypotheses were of interest to the experimenters. As is usually the case, the experimenters were not necessarily interested in whether the hypotheses were exactly true, but rather in how close they were to being true. to address these concerns, some Bayesian measures of the degree of departure from a linear hypothesis are considered. These measures are in the same spirit as the distance measure considered by Geisser (1967) in the linear discrimination problem. The problem of eliciting prior information from the experimenters is considered.

The problem of simultaneously deciding the signs of pparameters based on normally distributed estimators is considered. A decision that a parameter is too close to zero to decide its sign is allowed in order that the probability of at least one incorrect decision can be kept less than a preassigned value. Concepts of upper-convexity and local optimality are defined, and for p= 2 or 3 the locally optimal rules in the class of upper-convex rules are found. Critical values and operating characteristics are given for the locally optimal rule and some other plausible rules when p= 2.

An arbitrary finitely additive probability can be decomposed uniquely into a convex combination of a countably additive probability and a purely finitely additive (PFA) one. The coefficient of the PFA probability is an upper bound on the extent to which conglomerability may fail in a finitely additive probability with that decomposition. If the probability is defined on a σ-field, the bound is sharp. Hence, non-conglomerability (or equivalently non-disintegrability) characterizes finitely as opposed to countably additive probability. Nonetheless, there exists a PFA probability which is simultaneously conglomerable over an arbitrary finite set of partitions.

The problem of classifying an observation X into one of k multivariate normal distributions is considered. When samples are used to estimate the population parameters, the probabilities of correct classification, and the associated error rates, are random variables. Asymptotic expansions for the expected values and variances of these random variables, in terms of the inverses of the sample sizes, are found. Simulations have been performed to evaluate the expansions.