International Journal of Forecasting 4 (1988) 609-620 North-Holland

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BOOK REVIEWS

The International Journal of Forecasting Policy

The purposes of this section are to help our readers become aware of all books that are relevant to forecasting, and to emphasize those books making highly significant contributions.

The Book Reviews section will include a listing of Books Received and Reviews. Readers, authors and publishers are invited to contribute to the listings or to the reviews.

If you would like to do a review, please contact us first to determine whether a review is already being done. (For exceptional books, we may publish more than one review.) In preparing a review, please follow reference format given in the ‘Instructions to Authors’. The book reviews are being handled as follows:

North and South America: Rest of the world: Steven P. Schnaars Nigel Meade Baruch College Imperial College of Science and Technology The City University of New York Department of Management Science 17 Lexington Avenue Exhibition Road NEW YORK, NY 10010 LONDON SW7 2BX USA UK

J.M. Bernardo, M.H. DeGroot, D.V. Lindley and A.F.M. Smith (eds.), Bayesian Statistics Two: Proceedings of the Second Valencia International Meeting on Bayesian Statistics, 6-10 September. 1983 (North-Holland, Amsterdam, 1985) pp. 770, $75.

This volume comprises the proceedings of the Second International Meeting on Bayesian statistics held near Valencia, Spain in September 1983. (The proceedings provide a fair overview of research activities in Bayesian statistics as of September 1983.) The Proceedings cover a range of interesting applications and case studies. The coverage can be gauged from the contents list which details the 27 invited papers, each with lengthy and thorough contributions from discussants, and a selection of 18 of the many submitted papers at the conference. As might be expected from a volume of over 750 pages, there should be something here of interest to statisticians from all branches of the subject, whether their interests be primarily in philosophical/ foundational areas, decision analysis, theoreti- cal modelling, data analysis, or applications.

Much of Bayesian statistics focuses primarily on the formation of predictive statements, or forecasts, and thus the proceedings should be of interest to the forecasting community in general as well as statisticians. In this review I comment on several papers that are directly concerned with forecasting, as it is usually understood.

Of primary interest are several papers with problems of individuals and group probability assessments. A canonical example involves forecasters as they provide their subjective probability forecasts for the occurrence, or otherwise, of a single future event, such as rain on a given day.

0169-2070/M/$3.50 fi’\ 1988, Elscvier Science Pubhshers B.V. {North-Holland)

CIlil Booh review

DeGroot and Eriksson discuss the concepts of calibration and refinement. describing how these concepts Illay be used in the process of evalurrtion and comparison of two or more forecasters, ‘experts', or forecasting models. From a practical viewpoint. the discussion of decision-theoretic implications of the concepts, in the paper and in a discussion by Spiegelhalter, highlights the need for refinement among well-calibrated forecasters. Spiegelhalter also provides an interesting application in medical diagnosis, comparing a clinician’s forecasts with those of computer models.

Lindley takes a different view of t-his problem. In his paper, Lindley’s previous work on reconciliation is extended to the case of evaluation and combination of discrete probability forecast distributions from several individuals. The basic Bayesian concept is that such probabilities are to be taken by an observer as data, to be processed, in more or less standard ways, by a statistical model. A key concern is the development of suitable models of the correlation structure of the forecasts. Lindley’s multivariate log-normal models provide for such structure although, as the paper discusses, practical experience with assessment and estimation is needed.

The review paper by French is largely concerned with the same problems and models as Lindley, although it covers approaches for combining probability forecasts and the formation of group decisions. French largely agrees with Lindely that the only sound ‘aggregation framework involves an observer, chairman or other external agent collating individual forecasts and using them as data in arriving at his/her own posterior view of the uncertain quantities of interest.

Two case studies in forecast assessment and combination are given by Press and by Pratt and Schlaifer. Press reports an experiment in which a large number of subjects specify probability forecasts for events relating to the possibility of nuclear war. Press uses qualitative controlled feedback to correct for biases. He then treats the adjusted forecasts as a sample from a population distribution of opinion, estimating this distribution using density estimation fechniques. This approach lacks the foundational basis of others, such as Lindley’s, although, quoting Goldstein in discussion, ‘The paper concerns such a chilling issue that technical queries are perhaps irrelevant’. Conceptual issues highlighted include coherency checks on subjects, and difficulties in assessing very small probabilities. Pratt and Schlaifer present a large data set comprising percentile forecasts of gross receipts at each of two theatres over a 16-month period, together with actual values. Various aspects of the relationships among assessed percentiles and actual values are discussed using exploratory non-Bayesian data analytic techniques. This is an interesting data set and there is some illuminating discussion that may prove useful background information for forecasters who undertake similar studies of calibration and comparison.

A small number of papers concern time series forecasting directly, and those by Harrison and Ameen and by Migon and Harrison will be of key interest to anyone interested in the growing field of Bayesian forecasting using dynamic models. Harrison and Ameen relate the dynamic structure of standard dynamic linear (and non-linear) models to simple and widely accepted concepts of information discounting (EWWA, EWR, etc.). The paper also develops mathematical results linking discount Bayesian models to standard AREMA processes. Mathematics not withstanding, the novel discount concepts for structuring dynamic linear models represents a major breakthrough in communication and parsimony for forecasters using dynamic models. The modified discount concept provides a simple way of specifying the stochastic evolution of components of a time series model, by specifying a single discount factor for each component. Practitioners have become increasingly interested in Bayesian methods in recent years; the simplification of 0per;ltior-r offered by the discount approach should encourage this interest. Equally encouraging would be the availability of suitable computer software. a point mentioned in the paper.

Migon and Harrison report on Bayesian forecasting using nonlinear dynamic models in a case study concerning the relationship between consumer awareness and television advertising. This is a

significant aPPlication of many important, yet little used, techniques including feed-forward inter-

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vention, stochastic transfer function lnodelling, and non-linear Bayesian estimation within a class of non-normal models. Other contributions to time series analysis appear in papers by Jaynes, Polasek and Zellner. Jaynes discusses the effects of highly informative priors in seasonal models, and Zellner review the state of the art (circa 1983) of Bayesian analysis in econometrics. Polasek analyses seasonal distributed log models using hierarchical models to specify prior distributions. An im- portant feature of his paper is the systematic exploration of sensitivity to prior assumptions using extreme bounds analysis, a technique receiving growing attention among econometricians. Model choice and the choice of regression variables, is a problem central to many forecasting problems. Bernard0 and Bermudez discuss the selection of variables in probabilistic classification using a decision-theoretic approach that many statisticians would now accept as the “correct” method of model selection. There are computational problems with the approach, but its utility is demonstrti&ed in the prediction of election results. Kokalakis discusses related problems. Within a regression modelling context, Geisser reviews the predictive approach to modelling and diagnostics. Related ideas on robustness are dealt with by Pettit and Smith. West discuss modeling issues in generalized linear models and O’Hagan is concerned with hierarchical models.

There are many more papers in this volume that are of general interest to forecasters. Papers by Winkler present insights on information loss and problems of over-precision when data that are assumed to be independent are actually dependent. Similarly important papers are by: Goldstein who discusses foundational questions about the evolution of subjective beliefs and related coherence issues; Dempster who discusses his belief in the need for a wider view of Bayesian analysis than that embodied in the standard prior/likelihood/posterior paradigm; Hill et al., who develop new models for predicting survival limits of cancer patients; and Jewel1 who is concerned with predicting faults in a product. A point of general interest is that, in spite of a large number of applied papers, numerical/computational aspects recei ‘ve re. stively little coverage, as in the papers on Monte Carlo integration by Stewart and by Van Dijk and Kloek. This important area for Bayesian research is sure .to be a highlight of the proceeding of the 1987 conference.

In conclusion, anyone with a serious interest in modern Bayesian statistics should read these Proceedings, The papers provide a thorough and stimulating overview of the mainstream activities in the subject during the early 1980s much of which will find use as reference material for established researchers and students alike. I have no doubt that many statisticians, having read this volume, are eagerly anticipating the next in the series.

Mike West Udersitj~ of Warwick

Alan V. Deardoff and Robert M. Stern, The Michigan Model of World Production and Trade: Theory and Application (MIT Press, Cambridge, Massachusetts and London. 1986) pp. 272, $32.50, E29.25.

The MIT Press offers the reader a change to be acquainted with a series of books on theories of international trade, the resulting models, and their practical application [see e.g. Whalley (1984). Srinivasan and Whalley (1986)].

The book by A. Deardoff and R. Stern is a new volume in this series. The authors are well known to readers familiar with publications devoted to international trade modelling.

The book contains the results of the ten-year period, 1974-84, of research work on the Michigan Model. The authors repeatedly stress the fact that their primary concern was to supply a convenient