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Interpreting multivariate data. Proceedings of the Conference on Looking at Multivariate Data held in the University of Sheffield, Sheffield, March 24-27, 1980. (English) Zbl 0597.62002

Wiley Series in Probability and Mathematical Statistics. Chichester etc.: John Wiley & Sons Ltd. XVI, 374 p. (1981).
This volume is a collection of seventeen invited papers presented to the second of two major conferences held at the University of Sheffield in March 1980. [Papers from the first conference, entitled ”Graphical methods in statistics”, were published individually in Biometrika and J. R. Stat. Soc., Ser. C] The papers have been revised by the authors themselves, and hence take account of the discussion, and have also been closely edited by the general editor.
The title conveys well the style and outlook of the authors, which is very uniform and consistent. The emphasis is on exploring multivariate data in an attempt to make it comprehensible to the human observer either for the informal interpretation of any structure and form which may be present or as a basis for more sophisticated analysis and modelling. The methods put forward for doing this are to a very large extent graphical (both in the sense of automated visual display and of diagrammatic representation of relationships) and associated computational procedures. Details of the very considerable hardware and software support usually required are generally not discussed. The phrase ”multivariate data” is very broadly understood, and is not limited to data from continuous multivariate distributions as in classical ”multivariate analysis”. For example, multiway frequency tables are considered.
The papers are loosely divided into four sections. The titles largely convey the areas covered, but in some cases a short additional comment seems useful. Papers 1, 2 and 3, and papers 10, 11 and 12 form what are called two ”linked sets”, and complement each other; also papers 6, 7 and 8 discuss similar material, with minor overlap.
Contents: Part I: Methods for investigating bivariate data. 1. Peeling bivariate data by P. J. Green (pp. 3-19). 2. A brief description of nearest neighbour interpolation by R. Sibson (pp. 21-36) considers functions of two variables defined by a set of sample points in the plane, and their presentation. 3. Density estimation for univariate and bivariate data by B. W. Silverman (pp. 37-53). 4. Some graphical methods in the analysis of spatial point patterns by P. J. Diggle (pp. 55-73). 5. The statistics of shape by D. G. Kendall (pp. 75- 80) reports some new ideas for the representation of ”shape”, principally in two dimensions.
Part II: Reduction, display and analysis of data matrices and multiway tables. 6. Expressing complex relationships in two dimensions by J. C. Gower and P. G. N. Digby (pp. 83-118) discusses the biplot, correspondence analysis, scaling, asymmetric square tables, procrustes analysis, ordination. 7. Practical correspondence analysis by M. J. Greenacre (pp. 119-146). 8. Biplot display of multivariate matrices for inspection of data and diagnosis by K. R. Gabriel (pp. 147-173). 9. Statistical applications of real-time interactive graphics by D. F. Andrews (pp. 175-185).
Part III: Graphical display of data sets in 3 or more dimensions. 10. Preparation; prechosen sequences of views of P. A. Tukey and J. W. Tukey (pp. 189-213). 11. Data-driven view selection; agglomeration and sharpening by P. A. Tukey and J. W. Tukey (pp. 215-243). 12. Summarization; smoothing; supplemented views by P. A. Tukey and J. W. Tukey (pp. 245-275).
Part IV: Specific methods and practical applications. 13. Plotting the optimum positions of an array of cortical electrical phosphenes by B. S. Everitt and J. C. Gower (pp. 279-287). 14. Analysing data from multivariate directed graphs: and application to social networks by S. E. Fienberg, M. M. Meyer and S. S. Wasserman (pp. 289-306). 15. Some graphical procedures for the preliminary processing of longitudinal data by H. Goldstein (pp. 307-319). 16. Interpreting archaeological data by I. Graham (pp. 321-333). 17. Bayesian approaches to multivariate structure by A. F. M. Smith and D. J. Spiegelhalter (pp. 335-348) discusses one- and two-sample mean problems, variance matrix problems, classification and transformations to normality from a Bayesian viewpoint.
Each paper is accompanied by its own specific references, which are also combined into a composite list at the end of the book. An additional bibliography of related books is given.

MSC:

62-07 Data analysis (statistics) (MSC2010)
62-02 Research exposition (monographs, survey articles) pertaining to statistics
62H99 Multivariate analysis
62-06 Proceedings, conferences, collections, etc. pertaining to statistics
65S05 Graphical methods in numerical analysis
00B25 Proceedings of conferences of miscellaneous specific interest