When a candidate model for data is nonidentifiable, conventional wisdom dictates that the model must be simplified somehow so as to gain identifiability. We explore two scenarios involving mismeasured variables where, in fact, model expansion, as opposed to model contraction, might be used to obtain identifiability. We compare the merits of model contraction and model expansion. We also investigate whether it is necessarily a good idea to alter the model for the sake of identifiability. In particular, estimators obtained from identifiable models are compared to those obtained from nonidentifiable models in tandem with crude prior distributions. Both asymptotic theory and simulations with Markov chain Monte Carlo-based estimators are used to draw comparisons. A technical point which arises is that the asymptotic behavior of a posterior mean from a nonidentifiable model can be investigated using standard asymptotic theory, once the posterior mean is described in terms of the identifiable part of the model only.

Any general textbook that discusses moment generating functions (MGFs) shows how to obtain a moment of positive-integer order via differentiation, although usually the presented examples are only illustrative, because the corresponding moments can be calculated in more direct ways. It is thus somewhat unfortunate that very few textbooks discuss the use of MGFs when it becomes the simplest, and sometimes the only, approach for analytic calculation and manipulation of moments. Such situations arise when we need to evaluate the moments of ratios and logarithms, two of the most common transformations in statistics. Such moments can be obtained by differentiating and integrating a joint MGF of the underlying untransformed random variables in appropriate ways. These techniques are examples of multivariate Laplace transform methods and can also be derived from the fact that moments of negative orders can be obtained by integrating an MGF. This article reviews, extends and corrects various results scattered in the literature on this joint-MGF approach, and provides four applications of independent interest to demonstrate its power and beauty. The first application, which motivated this article, is for the exact calculation of the moments of a well-known limiting distribution under the unit-root AR(1) model. The second, which builds on Stigler’s Galtonian perspective, reveals a straightforward, non-Bayesian constructive derivation of the Stein estimator, as well as convenient expressions for studying its risk and bias. The third finds an exceedingly simple bound for the bias of a sample correlation from a bivariate normal population, namely the magnitude of the relative bias is not just of order n⁻¹, but actually is bounded above by n⁻¹ for all sample sizes n≥2. The fourth tackles the otherwise intractable problem of studying the finite-sample optimal bridge in the context of bridge sampling for computing normalizing constants. A by-product of the joint-MGF approach is that positive-order fractional moments can be easily obtained from an MGF without invoking the concept of fractional differentiation, a method used by R. A. Fisher in his study of k statistics 45 years before it reappeared in the probability literature.

Given the public’s ever-increasing concerns about data confidentiality, in the near future statistical agencies may be unable or unwilling, or even may not be legally allowed, to release any genuine microdata—data on individual units, such as individuals or establishments. In such a world, an alternative dissemination strategy is remote access analysis servers, to which users submit requests for output from statistical models fit using the data, but are not allowed access to the data themselves. Analysis servers, however, are not free from the risk of disclosure, especially in the face of multiple, interacting queries. We describe these risks and propose quantifiable measures of risk and data utility that can be used to specify which queries can be answered and with what output. The risk–utility framework is illustrated for regression models.

From 1858 to 1860, the English naturalist and social activist Philip P. Carpenter toured North America. In April of 1859 he visited Montréal, Canada. Shocked by the sanitary conditions of the city, he wrote a paper that used statistical arguments to call for health reforms. Six years later he settled in Montréal and quickly became an active promoter of this cause. He began accumulating additional numerical evidence in support of his views.

In the aftermath of a cholera scare in 1866, Carpenter became the driving force behind the creation of the Montreal Sanitary Association. That same year he published a second, more detailed article that took advantage of the 1861 census data to analyze mortality rates in Montréal. He made further statistical investigations in 1869.

Unfortunately, Carpenter did not understand some of the subtleties associated with the analysis of vital statistics. An obscure bookkeeper, Andrew A. Watt, made a scathing public attack on both Carpenter’s data and his interpretation thereof. In a series of newspaper articles, Watt scrutinized systematically all of Carpenter’s writings, showing his faults and correcting them wherever he could.

Although Watt’s arguments were correct, the public was slow to understand them. The controversy continued through 1870. When the nature of Watt’s criticisms finally became better understood and Carpenter persisted with statistical arguments, the latter lost credibility and was abandoned by his own association.

Lawrence D. Brown was born on December 16, 1940 in Los Angeles, California. He obtained his Ph.D. in mathematics from Cornell University in 1964. He has been on the faculty of the University of California, Berkeley, Cornell University, Rutgers University and, most recently, the Wharton School of the University of Pennsylvania, where he holds the Miers Busch Professorship of Statistics. Professor Brown was President of the Institute of Mathematical Statistics in 1992–1993, Coeditor of The Annals of Statistics for 1995–1997 and gave the prestigious Wald Memorial Lectures in 1985. In 1990, Professor Brown was elected to the U.S. National Academy of Sciences. In 1993, Purdue University awarded him an honorary D.Sc. degree in recognition of his distinguished achievements, and in 2002 he was named winner of the Wilks Memorial Award of the American Statistical Association.

Professor Brown is probably best known for his extensive work on the admissibility of estimators of one or more parameters. He has also published research on a broad variety of other topics including general decision theory, sequential analysis, properties of exponential families, foundations of statistical inference, conditional confidence, interval estimation and Edgeworth expansions, and bioequivalence. His current interests include functional nonparametrics, analysis of census data and queuing theory as involved in the analysis of call-center data.