In real applications most experimental situations are influenced by a large number of different factors. In these settings the design of an experiment leads to challenging optimization problems, even if the underlying relationship can be described by a linear model. Based on recent research, this book introduces the theory of optimum designs for complex models and develops general methods of reduction to marginal problems for large classes of models with relevant interaction structures.

Graphical methods have played an important role in the statistical analysis of experimental data, but have not been used as extensively for experiment design, at least as it is presented in most design of experiments texts. Yet graphical methods are particularly attractive for the design of experiments because they exploit our creative right-brain capabilities. Creative activity is clearly important in any kind of design, certainly for the design ofan experiment. The experimenter must somehow select a set of run conditions that will meet the goals for a particular experiment in a...

The Athens Conference on Applied Probability and Time Series in 1995 brought together researchers from across the world. The published papers appear in two volumes. Volume I includes papers on applied probability in Honor of J.M. Gani. The topics include probability and probabilistic methods in recursive algorithms and stochastic models, Markov and other stochastic models such as Markov chains, branching processes and semi-Markov systems, biomathematical and genetic models, epidemilogical models including S-I-R (Susceptible-Infective-Removal), household and AIDS epidemics, financial...

The frontier images of America embrace endless horizons, majestic herds of native ungulates, and romanticized life-styles of nomadie peoples. The images were mere reflections of vertebrates living in harmony in an ecosystem driven by the unpre- dictable local and regional effects of drought, frre, and grazing. Those effects, often referred to as ecological "disturbanees," are rather the driving forces on which species depended to create the spatial and temporal heterogeneity that favored ecological prerequisites for survival. Alandscape viewed by European descendants as monotony interrupted...

Genetics mapping, physical mapping and DNA sequencing are the three key components of the human and other genome projects. Statistics, mathematics and computing play important roles in all three, as well as in the uses to which the mapping and sequencing data are put. This volume edited by key researchers Mike Waterman and Terry Speed reviews recent progress in the area, with an emphasis on the theory and application of genetic mapping.

This IMA Volume in Mathematics and its Applications MATHEMATICAL APPROACHES TO BIOMOLECULAR STRUCTURE AND DYNAMICS is one of the two volumes based on the proceedings of the 1994 IMA Sum mer Program on "Molecular Biology" and comprises Weeks 3 and 4 of the four-week program. Weeks 1 and 2 appeared as Volume 81: Genetic Mapping and DNA Sequencing. We thank Jill P. Mesirov, Klaus Schulten, and De Witt Sumners for organizing Weeks 3 and 4 of the workshop and for editing the proceedings. We also take this opportunity to thank the National Institutes of Health (NIH) (National Center for Human...

It has been known for a long time that there is a close connection between stochastic processes and orthogonal polynomials. For example, N. Wiener 112] and K. Ito 56] knew that Hermite polynomials play an important role in the integration theory with respect to Brownian motion. In the 1950s D. G. Kendall 66], W. Ledermann and G. E. H. Reuter 67] 74], and S. Kar lin and J. L. McGregor 59] established another important connection. They expressed the transition probabilities of a birth and death process by means of a spectral representation, the so-called Karlin-McGregor representation, in...

Bayesian and likelihood approaches to inference have a number of points of close contact, especially from an asymptotic point of view. Both approaches emphasize the construction of interval estimates of unknown parameters. Empirical Bayes methods have historically emphasized instead the construction of point estimates. In this volume researchers present recent work on several aspects of Bayesian, likelihood and empirical Bayes methods, presented at a workshop held in Montreal, Canada. The goal of the workshop was to explore the linkages among the methods, and to suggest new directions for...

The main subject of this book is the estimation and forecasting of continuous time processes. It leads to a development of the theory of linear processes in function spaces. Mathematical tools are presented, as well as autoregressive processes in Hilbert and Banach spaces and general linear processes and statistical prediction. Implementation and numerical applications are also covered. The book assumes knowledge of classical probability theory and statistics.

lengths, that could not be captured with univariate linear filters. Exam- ples of research in both directions can be found in Sims (1977), Lahiri and Moore (1991), Stock and Watson (1993), and Hamilton (1994) and (1989). Although the first approach is known to present serious limitations, the new and more sophisticated methods developed in the second approach (most notably, multivariate and nonlinear extensions) are at an early stage, and have proved still unreliable, displaying poor behavior when moving away from the sample period . Despite the fact that business cycle estimation is basic to...