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Modern Multivariate Statistical Analysis: A Graduate Course and Handbook
114
Paul REYNOLDS
Book
(ed.)
Distributed Simulation 1985: Proceedings of the Conference on Distributed Simulation 1985,24-26 January 1985, San Diego, California
Volume 15, No. 2 in: Simulation Series, Simulation Councils, La Jolla, 1985, viii + 111 pag= Distributed simulation is concerned with taking the simulation of a physical process and distributing it over a network of tightly coupled processors. It,is the most likely means by which the time and memory constraints often encountered in large scale simulation may be alleviated. The papers in these conference proceedings attempt to address the major issues relating to distributed simulation, where simulation covers the range from discrete event to continuous simulation. For discrete event simulation, two basic approaches for implementing distributed simulation appear to be popular. One is to take simulation support functions that are noninteractive and which can be executed in parallel as distributed tasks (e.g. random number generation, statistics collection, all user written event routines). The other is to take the basic processes being simulated and allocate each to a processor. This latter approach quite requently favoured in the papers, leans more naturally towards the process-based view of simulation structures. Protocols for handling message processing are proposed as well as the avoidance of deadlock. Frequent reference is made in these protocols for the need to ‘rollback the simulation when a new message appears from ‘the past’, and the simulation needs to be adjusted backwards to that point in time. Perhaps not surprisingly, most of the papers propose structures or methodologies for pursuing distributed simulation, but little practical evidence of its presumed success is given. Some work has been carried out with small prototypes or small problems, but nothing is reported concerning the problem of distributing large scale simulation models in anger. A variety of related topics are also covered, such as calculations of potential elapsed-time saving, a methodology for determining inherent parallelism in a simulation (and thereby the merits of using distributed simulation) and differential
Reviews
and algebraic equation solving by distributed methods. Automatic partitioning must be developed on parallel architectures to make distributed simulation worthwhile, but there are no known tractable optimal solutions for such partitioning. Methodologies for mapping discrete event models onto hierarchical simulations are proposed. Most papers in these proceedings are written from a computer scientist’s viewpoint rather than an operation researcher’s. Little practical evidence is given, the bulk of the papers being theoretical. However, anyone interested in the accomplishments and remaining problems associated with distributed simulation should not (and cannot) overlook these proceedings. R.J. PA UL London School of Economics London, United Kingdom
Minoru SIOTANI, Takesi HAYAKAWA Yasunori FUJIKOSHI
and
Modern Multivariate Statistical Analysis: A Graduate Course and Handbook
Volume 9 in: American Studies in Mathematical and Management Sciences, American Siences, Columbus, 1985, xiv + 759 pages, $39.50 A very nice book, to begin with, but . . . maybe not very interesting for the readership of this journal. According to the authors: “The aim of t,he book is to give the reader a modern theoretical account of multivariate analysis and to cultivate the readers’ abilities for sound theoretical treatment of multivariate problems. Thus this book assumes that the reader has knowledge from a multivariate methods course . . . ” This means that the book contains no applications, and, in my opinion, it is therefore only interesting for professors (and students) in this subject and for librarians. For whom it is intended, it is a very nice and clearly written book. The chapters are: 1. 2. 3. 4. 5. 6.
Multivariate normal and some other distributions. Wishart distribution and Functions of Wishart matrices. Regressions, correlations and their distributions. Useful asymptotic expansion formulas. Inference on mean vector and Hotelling’s statistic. Multiple comparisons on mean vectors.
Book
Multivariate regression and linear model. Inference on cqvariance matrices. 9. Discriminant analysis. 10. Distributions of characteristic roots and vectors. 11. Principal component analysis. 12. Canonical correlation analysis. 13. Selection of variables. Appendices A: Some results on matrices. B: Matrix derivation and Jacobians. C: Some specific computerprograms (70 pages). 7. 8.
I miss chapters about factor and cluster analysis. The book contains 70 pages of references (up to 1981).
115
Reviews
discussed in more general cases; hence, after studying the book, students are not able to understand the classical ‘Gaussian law of errors in physical measures’, which is in fact of a large use for everybody. It must be noted that the book contains two chapters introducing to elementary statistics, and one on artificial generation of random variables; and that many examples ‘and problems are presented, very well chosen, with discussions and short solutions. R. FORTET Laboratoire de Probabilitt!, Tour 56 75230 Paris, France
A.J. BOSCH Eindhoven University of Technology Eindhoven, Netherlands
Anatol RAPOPORT G.P. BEAUMONT Probability and Random Variables
Ellis Horwood, Chichester, 1986, 345 pages, 212.50
General System Theory: Essential Concepts and Applications
Volume 10 in: Cybernetics and Systems Series, Abacus, Tunbridge Wells, 1986, v+ 270 pages, E24.50
In schools and universities, there is often the. necessity of introducing to probability and statistics, students who have a limited background in mathematics. The present book is intended to face that uncomfortable situation. Of course, the exposition, however rigorous, does not pretend to full generality; for instance, the concept of continuous random variable is restricted, in order that computation of moments reduces to integrals of elementary Riemannian type. Incidentally, I qtiote that the author speaks of a probability density for discrete random variables, which is not really incorrect, but unusual. In a simple case only, the author deduces the law of large numbers from Tschebischev’s inequality; actually, he gets convergence in the quadratic mean, but reduces his proposition to the convergence in probability, without writing nor discussing the terms: law of large numbers, quadratic mean, in probability. Here, I point out that ordinary people-hence, ordinary students-expect to get some precise information about ‘law of large numbers’, which is a very popular term. Another point is that the central limit theorem, proved in the simplest case of identically distributed random variables, is not presented nor
“This new awareness of the fundamental relatedness of everything to everything else has been probably the most ‘practical’ result of the systems approach” (last sentence of the preface). “But prediction and control are not the only rewards of scientific cognition. Equally important, in fact, even more important in some areas are understanding and emancipation”.( ... . ). “Here General System Theory enters in its most important function, namely, making thinking in terms of analogies, the basis of all searching for ‘explanation’ (probably a basic human need) sharper, broader, and above all, disciplined, so as to satisfy the standards of scientific cognition. It is this input of GST into the ever growing storage of reliable and organized knowledge that ought to be regarded as the most valuable contribution of this approach” (last concluding remark, p. 259). The reader may expect that some work has to be done between these two sentences. A. Rapoport, mathematician and biologist, is surely one of the most informed authors to write about that work, since he has been with the G.S.T. since its foundation. But how is it done? “Since G.S.T. is not properly a ‘theory’ (this book, p. 220), nor does it provide an ‘inquiring
Paul REYNOLDS
Book
(ed.)
Distributed Simulation 1985: Proceedings of the Conference on Distributed Simulation 1985,24-26 January 1985, San Diego, California
Volume 15, No. 2 in: Simulation Series, Simulation Councils, La Jolla, 1985, viii + 111 pag= Distributed simulation is concerned with taking the simulation of a physical process and distributing it over a network of tightly coupled processors. It,is the most likely means by which the time and memory constraints often encountered in large scale simulation may be alleviated. The papers in these conference proceedings attempt to address the major issues relating to distributed simulation, where simulation covers the range from discrete event to continuous simulation. For discrete event simulation, two basic approaches for implementing distributed simulation appear to be popular. One is to take simulation support functions that are noninteractive and which can be executed in parallel as distributed tasks (e.g. random number generation, statistics collection, all user written event routines). The other is to take the basic processes being simulated and allocate each to a processor. This latter approach quite requently favoured in the papers, leans more naturally towards the process-based view of simulation structures. Protocols for handling message processing are proposed as well as the avoidance of deadlock. Frequent reference is made in these protocols for the need to ‘rollback the simulation when a new message appears from ‘the past’, and the simulation needs to be adjusted backwards to that point in time. Perhaps not surprisingly, most of the papers propose structures or methodologies for pursuing distributed simulation, but little practical evidence of its presumed success is given. Some work has been carried out with small prototypes or small problems, but nothing is reported concerning the problem of distributing large scale simulation models in anger. A variety of related topics are also covered, such as calculations of potential elapsed-time saving, a methodology for determining inherent parallelism in a simulation (and thereby the merits of using distributed simulation) and differential
Reviews
and algebraic equation solving by distributed methods. Automatic partitioning must be developed on parallel architectures to make distributed simulation worthwhile, but there are no known tractable optimal solutions for such partitioning. Methodologies for mapping discrete event models onto hierarchical simulations are proposed. Most papers in these proceedings are written from a computer scientist’s viewpoint rather than an operation researcher’s. Little practical evidence is given, the bulk of the papers being theoretical. However, anyone interested in the accomplishments and remaining problems associated with distributed simulation should not (and cannot) overlook these proceedings. R.J. PA UL London School of Economics London, United Kingdom
Minoru SIOTANI, Takesi HAYAKAWA Yasunori FUJIKOSHI
and
Modern Multivariate Statistical Analysis: A Graduate Course and Handbook
Volume 9 in: American Studies in Mathematical and Management Sciences, American Siences, Columbus, 1985, xiv + 759 pages, $39.50 A very nice book, to begin with, but . . . maybe not very interesting for the readership of this journal. According to the authors: “The aim of t,he book is to give the reader a modern theoretical account of multivariate analysis and to cultivate the readers’ abilities for sound theoretical treatment of multivariate problems. Thus this book assumes that the reader has knowledge from a multivariate methods course . . . ” This means that the book contains no applications, and, in my opinion, it is therefore only interesting for professors (and students) in this subject and for librarians. For whom it is intended, it is a very nice and clearly written book. The chapters are: 1. 2. 3. 4. 5. 6.
Multivariate normal and some other distributions. Wishart distribution and Functions of Wishart matrices. Regressions, correlations and their distributions. Useful asymptotic expansion formulas. Inference on mean vector and Hotelling’s statistic. Multiple comparisons on mean vectors.
Book
Multivariate regression and linear model. Inference on cqvariance matrices. 9. Discriminant analysis. 10. Distributions of characteristic roots and vectors. 11. Principal component analysis. 12. Canonical correlation analysis. 13. Selection of variables. Appendices A: Some results on matrices. B: Matrix derivation and Jacobians. C: Some specific computerprograms (70 pages). 7. 8.
I miss chapters about factor and cluster analysis. The book contains 70 pages of references (up to 1981).
115
Reviews
discussed in more general cases; hence, after studying the book, students are not able to understand the classical ‘Gaussian law of errors in physical measures’, which is in fact of a large use for everybody. It must be noted that the book contains two chapters introducing to elementary statistics, and one on artificial generation of random variables; and that many examples ‘and problems are presented, very well chosen, with discussions and short solutions. R. FORTET Laboratoire de Probabilitt!, Tour 56 75230 Paris, France
A.J. BOSCH Eindhoven University of Technology Eindhoven, Netherlands
Anatol RAPOPORT G.P. BEAUMONT Probability and Random Variables
Ellis Horwood, Chichester, 1986, 345 pages, 212.50
General System Theory: Essential Concepts and Applications
Volume 10 in: Cybernetics and Systems Series, Abacus, Tunbridge Wells, 1986, v+ 270 pages, E24.50
In schools and universities, there is often the. necessity of introducing to probability and statistics, students who have a limited background in mathematics. The present book is intended to face that uncomfortable situation. Of course, the exposition, however rigorous, does not pretend to full generality; for instance, the concept of continuous random variable is restricted, in order that computation of moments reduces to integrals of elementary Riemannian type. Incidentally, I qtiote that the author speaks of a probability density for discrete random variables, which is not really incorrect, but unusual. In a simple case only, the author deduces the law of large numbers from Tschebischev’s inequality; actually, he gets convergence in the quadratic mean, but reduces his proposition to the convergence in probability, without writing nor discussing the terms: law of large numbers, quadratic mean, in probability. Here, I point out that ordinary people-hence, ordinary students-expect to get some precise information about ‘law of large numbers’, which is a very popular term. Another point is that the central limit theorem, proved in the simplest case of identically distributed random variables, is not presented nor
“This new awareness of the fundamental relatedness of everything to everything else has been probably the most ‘practical’ result of the systems approach” (last sentence of the preface). “But prediction and control are not the only rewards of scientific cognition. Equally important, in fact, even more important in some areas are understanding and emancipation”.( ... . ). “Here General System Theory enters in its most important function, namely, making thinking in terms of analogies, the basis of all searching for ‘explanation’ (probably a basic human need) sharper, broader, and above all, disciplined, so as to satisfy the standards of scientific cognition. It is this input of GST into the ever growing storage of reliable and organized knowledge that ought to be regarded as the most valuable contribution of this approach” (last concluding remark, p. 259). The reader may expect that some work has to be done between these two sentences. A. Rapoport, mathematician and biologist, is surely one of the most informed authors to write about that work, since he has been with the G.S.T. since its foundation. But how is it done? “Since G.S.T. is not properly a ‘theory’ (this book, p. 220), nor does it provide an ‘inquiring