Applied Multiway Data Analysis

Book Reviews are involved in the analysis of non-linear time series data. Sreenivasan Ravi University of Mysore E-mail: [email protected] Credit Risk Management: Basic Concepts, Financial Risk Components, Rating Analysis, Models, Economic and Regulatory Capital T. van Gestel and B. Baesens, 2009 Oxford, Oxford University Press xvi + 536 pp., £75.00 ISBN 978-0-199-54511-7 Current international turmoil in the banking and financial industry makes the publication of this book so timely. The authors bring with them an invaluable insight in the practical working of the Basel Committee on capital adequacy at the Bank for International Settlements and in how the financial industry is changing its methods of measurement and reporting credit risk. It begins with an extensive overview of the material that is covered in the book with an inclusive review of terminology. Credit scoring is described in detail but without calculus. This book is not a manual for credit scoring; it rather gives a detailed account of how it is used in practice. As explained by the authors, default risk depends on definitions of loss and they follow closely the Basel Committee’s recommendations. This reference makes definitions of loss consistent and comparisons between rating institutions coherent. Having covered core topics on credit risk scoring, rating and measurement, Chapter 5, on applications to portfolio risk measurement, provides practical tools for industry professionals. Finally the book ends with a welcome chapter on the Basel Committee and its implication for credit risk management. For quantitatively minded readers there is a wide range of ideas that are useful for developing routines and scoring systems; existing practices are also well covered. One cannot help noticing that credit risk calculation is as much a science as it is an art. Quantitative analysis involves calculating probabilities of default from available and published data, either in balance sheet form or other published reports. The art is in building rating systems to calculate probabilities of default and loss given default whereas the scientific and perhaps more correct quantitative value-free calculations use both economic and statistical theory in structural models for evaluation of rating and scoring systems. This book mainly discusses a financial industry perspective by professionals from the banking and 941 financial services. It is an intermediate book between theory, i.e. a textbook treatment of the subject, and a manual for risk management. Courses that could adopt this title include money and banking, and financial management as well as risk management; besides, it is surely a main reference for practitioners who are interested in risk rating methods. Morteza Aalabaf-Sabaghi Economic Cooperation Organizations College of Insurance Tehran E-mail: [email protected] Applied Multiway Data Analysis P. M. Kroonenberg, 2008 Hoboken, Wiley xxii + 580 pp., £62.15 ISBN 978-0-470-16497-6 This is an authoritative and ambitious text dealing with the analysis of multiway tables—defined by the author as data consisting of not only rows and columns but also an additional dimension which could perhaps have arisen from collecting a number of observations on subjects in different environments (such as with genotype–environment interaction experiments in agriculture) or at different time points in a longitudinal study. There is a wealth of supporting information available from http://three-mode.leidenuniv. nl/, and this appears to be an area of investigation that is currently growing in a range of natural and social science applications. The varying nature of multiway data is covered throughout the text, and a solid if slightly introductory coverage is given to the model fitting algorithms. The author seems to concentrate essentially on Tucker and Parafac models. This is perhaps one of the few reservations that can be made about the book, and it is a point which is emphasized by the author, who acknowledges that it concentrates on those areas of three-mode analysis with which he is most familiar (and has made several contributions to the literature). Other methods, such as STATIS, receive brief mention, whereas other approaches such as common principal components (which does continue to receive some attention in the literature) or mixtures of factor analysers (which are very well covered in the literature) do not feature strongly. However, in a book of 578 pages, some selection of material had to take place. The intended audience is perhaps those working in the social or natural sciences who wish to attempt an analysis of multiway data, using Tucker or Parafac models. As such, there is guidance on 942 Book Reviews preprocessing the data (centring and scaling data cease to be trivial in multiway data), and ways of approaching different kinds of data (ratio scale, or Likert or bipolar scaled data) are discussed. Missing data received a brief chapter, but rather more coverage is given to model selection, interpretation and residual analysis. In the author’s own words ‘Substantive interpretation of the parameters of component models is seldom straightforward’; this understates a reservation that many have about these approaches to data analysis. All topics are well illustrated with good examples from a fairly wide range of applications (perhaps tending towards social sciences). The book’s usefulness is enhanced by a glossary of multiway terminology, a good index and references to extension work (such as multiway cluster analysis and robustness). This is a well-crafted and highly readable book. Paul Hewson University of Plymouth E-mail: [email protected] Polya Urn Models H. M. Mahmoud, 2009 Boca Raton, Chapman and Hall–CRC 290 pp., $79.95 ISBN 978-1-420-05983-0 Since the classical treatise by Johnson and Kotz (1977), many new results and applications of urn models have been developed. This timely monograph presents an overview of the current state of this field. It is not a book for beginners, even though the first two chapters develop much of discrete probability ab initio via urn models. Familiarity with the content of (at least) a Bachelor’s degree that includes standard probability distributions, and the different ideas of convergence of random variables, is assumed. All 10 chapters end with a set of exercises, with full solutions over 43 pages. The main focus is on models where balls take one of k different colours. At each drawing, one ball is selected completely at random from the urn: suppose that its colour is i. This ball is then returned to the urn, along with Aij balls of colour j .j = 1, 2, . . . , k/. The matrix A = .Aij / is termed a schema; its entries are necessarily integers, but they may take negative values. Interest is on the development of the urn’s composition, especially asymptotic results, so there are strong restrictions on the form of A, to ensure that the process can continue indefinitely, whatever balls are drawn—the model must be tenable. Much of the book addresses the case k = 2, with Wn white balls and Bn blue balls after n drawings. In Polya’s original model, s balls of the colour drawn were added. Friedman’s model is the same, except that a balls of the other colour are also added; the Bagchi–Pal model is when A is tenable, and both row sums are equal, which ensures that the total number of balls in the urn after n drawings is fixed. Chapter 3 gives asymptotic results for (Wn , Bn /: even these initial models show the need for excellent manipulative skills. Chapter 4 embeds the process in continuous time, by taking each ball, independently, to be drawn after a random time having an exponential distribution with unit mean—Poissonization. The memoryless property of this distribution simplifies matters—after each drawing and replacement, the balls in the urn still wait independent E(1) times for selection. Frequently, the time of the nth drawing turns out to have a distribution that is concentrated near its mean. That implies that de-Poissonization, i.e. extracting a discrete process from one in continuous time, is fairly straightforward, as shown in the next chapter. Chapter 6 considers urns where the schema has random entries. Under strict conditions on the eigenvalues of the matrix of mean values, laws of large numbers and asymptotic central limit theorems are found. This is followed by an account of recent work using a combinatorial approach and generating functions, rather than direct probabilistic methods. Two chapters discuss applications in respectively informatics and the biosciences. The final chapter dips briefly into models where more than one ball at a time may be extracted. This book is attractively produced and looks to have been very carefully proofread—essential, given the complexity of many expressions. It has achieved its aim of being a readable and comprehensive account of the current state of the field. Reference Johnson, N. and Kotz, S. (1977) Urn Models and Their Applications. New York: Wiley. John Haigh University of Sussex Brighton E-mail: [email protected] Computational Statistics Handbook with MATLAB, 2nd edn W. L. Martinez and A. R. Martinez, 2008 Boca Raton, Chapman and Hall–CRC xxiv + 768 pp., $80.96 ISBN 1-584-88566-1 This book was designed with the twin objectives of making statistical techniques available to a