Here are two books on a topic new to Technometrics: statistical and mathematical demography. The first author of Applied Mathematical Demography wrote the first two editions of this book alone. The second edition was published in 1985. Professor Keyfritz noted in the Preface (p. vii) that at age 90 he had no interest in doing another edition; however, the publisher encouraged him to find a coauthor. The result is an additional focus for the book in the world of biology that makes it much more relevant for the sciences. The book is now part of the publisher’s series on Statistics for Biology and Health. Much of it, of course, focuses on the many aspects of human populations. The new material focuses on mature population models, the particular focus of the new author (see, e.g., Caswell 2000). As one might expect from a book that was originally written in the 1970s, it does not include a lot of information on statistical computing. The new book by Alho and Spencer is focused on putting a better emphasis on statistics in the discipline of demography (Preface, p. vii). It is part of the publisher’s Series in Statistics. The authors are both statisticians, so the focus is on statistics as used for demographic problems. The authors are targeting human applications, so their perspective on science does not extend any further than epidemiology. The book actually strikes a good balance between statistical tools and demographic applications. The authors use the first two chapters to teach statisticians about the concepts of demography. The next four chapters are very similar to the statistics content found in introductory books on survival analysis, such as the recent book by Kleinbaum and Klein (2005), reported by Ziegel (2006). The next three chapters are focused on various aspects of forecasting demographic rates. The book concludes with chapters focusing on three areas of applications: errors in census numbers, financial applications, and small-area estimates.

Univariate Discrete Distributions

This report summarizes a variety of the most useful and commonly applied methods for obtaining Dempster-Shafer structures, and their mathematical kin probability boxes, from empirical information or theoretical knowledge. The report includes a review of the aggregation methods for handling agreement and conflict when multiple such objects are obtained from different sources.

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Constructing Probability Boxes and Dempster-Shafer Structures

Introduction.- Vector and Matrix Algebra.- The Multivariate Normal Distribution, Multivariate Normality, and Covariance Structure.- One- and Two-Sample Tests.- Multivariate Analysis of Variance.- Discriminant Analysis.- Canonical Correlation.- Principal Component Analysis.- Factor Analysis.- Structural Equations.

Applied Multivariate Analysis

Computational statistics & data analysis

This review examines the state of Bayesian thinking as Statistics in Medicine was launched in 1982, reflecting particularly on its applicability and uses in medical research. It then looks at each subsequent five-year epoch, with a focus on papers appearing in Statistics in Medicine, putting these in the context of major developments in Bayesian thinking and computation with reference to important books, landmark meetings and seminal papers. It charts the growth of Bayesian statistics as it is applied to medicine and makes predictions for the future. From sparse beginnings, where Bayesian statistics was barely mentioned, Bayesian statistics has now permeated all the major areas of medical statistics, including clinical trials, epidemiology, meta-analyses and evidence synthesis, spatial modelling, longitudinal modelling, survival modelling, molecular genetics and decision-making in respect of new technologies.

Bayesian statistics in medicine: a 25 year review

We give new necessary and sufficient conditions for the existence of a common solution to the pair of linear matrix equations A1XB1 = C1 and A2XB2 = C2 and derive a new representation of the general common solution to these two equations. We apply this result to determine new necessary and sufficient conditions for the existence of an Hermitian solution and a representation of the general Hermitian solution to the matrix equation AXB = C.

A representation of the general common solution to the matrix equations A1XB1 = C1 and A2XB2 = C2 with applications

A comparison of asymptotic error rate expansions for the sample linear discriminant function

Confidence intervals for a binomial parameter based on binary data subject to false-positive misclassification

Response misclassification of counted data biases and understates the uncertainty of parameter estimators in Poisson regression models. To correct these problems, researchers have devised classical procedures that rely on asymptotic distribution results and supplemental validation data in order to estimate unknown misclassification parameters. We derive a new Bayesian Poisson regression procedure that accounts and corrects for misclassification for a count variable with two categories. Under the Bayesian paradigm, one can use validation data, expert opinion, or a combination of these two approaches to correct for the consequences of misclassification. The Bayesian procedure proposed here yields an operationally effective way to correct and account for misclassification effects in Poisson count regression models. We demonstrate the performance of the model in a simulation study. Additionally, we analyze two real-data examples and compare our new Bayesian inference method that adjusts for misclassification with a similar analysis that ignores misclassification.

A Bayesian approach to adjust for diagnostic misclassification between two mortality causes in Poisson regression.

The sample linear discriminant function (LDF) is known to perform poorly when the number of features p is large relative to the size of the training samples, A simple and rarely applied alternative to the sample LDF is the sample Euclidean distance classifier (EDC). Raudys and Pikelis (1980) have compared the sample LDF with three other discriminant functions, including thesample EDC, when classifying individuals from two spherical normal populations. They have concluded that the sample EDC outperforms the sample LDF when p is large relative to the training sample size. This paper derives conditions for which the two classifiers are equivalent when all parameters are known and employs a Monte Carlo simulation to compare the sample EDC with the sample LDF no only for the spherical normal case but also for several nonspherical parameter configurations. Fo many practical situations, the sample EDC performs as well as or superior to the sample LDF, even for nonspherical covariance configurations.

Dean M. Young

Papers

A representation of the general common solution to the matrix equations A1XB1 = C1 and A2XB2 = C2 with applications

A comparison of asymptotic error rate expansions for the sample linear discriminant function

Confidence intervals for a binomial parameter based on binary data subject to false-positive misclassification

A Bayesian approach to adjust for diagnostic misclassification between two mortality causes in Poisson regression.

The Euclidean distance classifier: an alternative to the linear discriminant function