Aust. N. Z. J. Stat. 53(3), 2011, 389–396 doi: 10.1111/j.1467-842X.2011.00612.x BOOK REVIEWS Biplots in Practice. By Michael Greenacre. Fundaci ´ on, BBVA, Bilbao, Spain. 2010. 237 pages. €32.00 (paperback). ISBN 978-8-4923-8468-6. Originally proposed by Gabriel (1971), biplots have gained widespread attention as a means of providing a graphical interpretation of a variety of statistical problems. While scatterplots provide the user with a means of visualizing the association between two numerical variables, biplots have been used extensively in a variety of multivariate situations (including the analysis of categorical data), and much has been much written on their construction and interpretation. As a late 2010 contribution to this topic, Michael Greenacre’s Biplots in Practice provides an introductory, non-technical and easy to read description of biplots to a variety of popular statistical techniques. Greenacre is better known for his influence in correspondence analysis, and more recently biplots, and many readers will have benefited from his expertise in these areas during his visits to Australia over the past few years. Greenacre states in his preface (p. 11) that ‘this book is divided into short chapters for ease of self-learning or for teaching ... and is aimed at the widest possible audience in all areas of research ... ’. Therefore for those requiring an introduction to some of the fundamentals of biplots, Biplots in Practice is a very good place to start. As we shall describe, the book fills a hole left by those contributions that provide a more detailed and often theoretical treatment of the topic. The book begins with an overview of the geometric nature of biplots and does so using notation not dissimilar to that of introductory vector analysis (Chapter 1). A brief discussion of regression analysis is made in Chapter 2, where Gabriel’s (1971) matrix decomposition is introduced. Chapter 3 extends this idea by demonstrating the applicability of biplots for generalized linear models, including logistic regression. While these chapters provide a good demonstration of the link between biplots and these models, there is no discussion in the chapters of what role the assumptions imposed upon the residuals have on the analysis (if any). Interestingly, the issue of residuals is not discussed until the book’s epilogue (p. 217), where least-squares estimation is described as a possible solution to the biplot decomposition. A simple description of how one can use biplots for multi-dimensional scaling is given in Chapter 4. As a means of reducing the number of dimensions needed to visualize multivariate data, sin- gular value decomposition (SVD) is central to multivariate data analysis, and Biplots in Practice looks at the properties of SVD in Chapter 5. In particular, descriptions of generalized singular vectors and singular vectors are given, as are principal coordinates, which allow a visual description of the data for any centred matrix while taking into account the variation contained within it. More specific applications of biplots to commonly considered multivariate data analysis techniques follow in subsequent chapters. Chapter 6 considers the use of biplots for principal component analysis, while Chapter 7 describes their use in log-ratio analysis, a topic considered in Greenacre (2009, 2010). The next three chapters look at biplots and briefly describe their use in the correspondence analysis of two-way contingency tables (Chapter 8) and of multi-way contingency tables (Chapters 9 and 10). Taking into consideration the purpose of the book, it is not surprising that these chapters provide only the merest glance at these topics, although a more comprehensive discussion can be found in Greenacre (1993). The book goes on to describe the application of biplots to discriminant analysis and canonical correspondence analysis (or constrained correspondence analysis). The last three chapters are interesting and provide a practical application of the above techniques to biomedicine, socio-economics and ecology. Greenacre has ex- tensive experience in the application of multivariate techniques (especially correspondence analysis), and so it is no surprise that these chapters provide a very good practice demonstration of biplots in a variety of situations. There are four appendices to the book, all of which are interesting for different reasons. The first of these gives some very simple R commands to perform each of the techniques described in the previous chapters. The code is easy to follow and colour-coded for ease of use. However, for some chapters, there are commands that need to be imported prior to conducting these analyses. For example, the appendix C 2011 Australian Statistical Publishing Association Inc. Published by Blackwell Publishing Asia Pty Ltd. Australian & New Zealand Journal of Statistics
Transcript
Aust. N. Z. J. Stat. 53(3), 2011, 389–396 doi: 10.1111/j.1467-842X.2011.00612.x
BOOK REVIEWS
Biplots in Practice. By Michael Greenacre. Fundacion, BBVA, Bilbao, Spain. 2010. 237 pages. €32.00(paperback). ISBN 978-8-4923-8468-6.
Originally proposed by Gabriel (1971), biplots have gained widespread attention as a means of providinga graphical interpretation of a variety of statistical problems. While scatterplots provide the user with ameans of visualizing the association between two numerical variables, biplots have been used extensivelyin a variety of multivariate situations (including the analysis of categorical data), and much has beenmuch written on their construction and interpretation. As a late 2010 contribution to this topic, MichaelGreenacre’s Biplots in Practice provides an introductory, non-technical and easy to read descriptionof biplots to a variety of popular statistical techniques. Greenacre is better known for his influencein correspondence analysis, and more recently biplots, and many readers will have benefited from hisexpertise in these areas during his visits to Australia over the past few years.
Greenacre states in his preface (p. 11) that ‘this book is divided into short chapters for ease ofself-learning or for teaching . . . and is aimed at the widest possible audience in all areas of research . . . ’.Therefore for those requiring an introduction to some of the fundamentals of biplots, Biplots in Practiceis a very good place to start. As we shall describe, the book fills a hole left by those contributions thatprovide a more detailed and often theoretical treatment of the topic.
The book begins with an overview of the geometric nature of biplots and does so using notation notdissimilar to that of introductory vector analysis (Chapter 1). A brief discussion of regression analysisis made in Chapter 2, where Gabriel’s (1971) matrix decomposition is introduced. Chapter 3 extendsthis idea by demonstrating the applicability of biplots for generalized linear models, including logisticregression. While these chapters provide a good demonstration of the link between biplots and thesemodels, there is no discussion in the chapters of what role the assumptions imposed upon the residualshave on the analysis (if any). Interestingly, the issue of residuals is not discussed until the book’s epilogue(p. 217), where least-squares estimation is described as a possible solution to the biplot decomposition.
A simple description of how one can use biplots for multi-dimensional scaling is given inChapter 4. As a means of reducing the number of dimensions needed to visualize multivariate data, sin-gular value decomposition (SVD) is central to multivariate data analysis, and Biplots in Practice looksat the properties of SVD in Chapter 5. In particular, descriptions of generalized singular vectors andsingular vectors are given, as are principal coordinates, which allow a visual description of the data forany centred matrix while taking into account the variation contained within it. More specific applicationsof biplots to commonly considered multivariate data analysis techniques follow in subsequent chapters.Chapter 6 considers the use of biplots for principal component analysis, while Chapter 7 describes theiruse in log-ratio analysis, a topic considered in Greenacre (2009, 2010). The next three chapters lookat biplots and briefly describe their use in the correspondence analysis of two-way contingency tables(Chapter 8) and of multi-way contingency tables (Chapters 9 and 10). Taking into consideration thepurpose of the book, it is not surprising that these chapters provide only the merest glance at thesetopics, although a more comprehensive discussion can be found in Greenacre (1993). The book goeson to describe the application of biplots to discriminant analysis and canonical correspondence analysis(or constrained correspondence analysis). The last three chapters are interesting and provide a practicalapplication of the above techniques to biomedicine, socio-economics and ecology. Greenacre has ex-tensive experience in the application of multivariate techniques (especially correspondence analysis),and so it is no surprise that these chapters provide a very good practice demonstration of biplots in avariety of situations.
There are four appendices to the book, all of which are interesting for different reasons. The first ofthese gives some very simple R commands to perform each of the techniques described in the previouschapters. The code is easy to follow and colour-coded for ease of use. However, for some chapters, thereare commands that need to be imported prior to conducting these analyses. For example, the appendix
provides a simple demonstration of how R can be used to undertake a correspondence analysis of dataand construct a biplot from it. However the user must first import and be familiar with Greenacre’s code,which he described in far more detail a few years ago – see Nenadic & Greenacre (2007). Appendix Bis a bibliography (there is no reference list given in the book) of some of the key (albeit predominatelyEuro-centric) contributions to the development of biplots and multivariate statistics. Appendix C givesa helpful glossary of terms, and Appendix D includes an epilogue in which Greenacre provides his‘personal opinions about biplots’ – although it could easily have been written as an objective accountof several issues not described in the earlier chapters.
While writing this review, there were a number of questions I wanted to keep in mind. First, ‘isthere anything really new in the book?’ Unfortunately, no: it has all been done elsewhere (much of itby Greenacre in his extensive contributions to multivariate analysis, some of which are listed in thebibliography) and in far more detail. The book does, however, link together well the fundamental aspectsof the topics covered in a non-technical, descriptive and charming way. I also considered whether thebook is interesting. I would have to say cautiously that it is, but only for those not wishing to be given adeep and theoretical account of its uses. Biplots in Practice perfectly complements Greenacre’s earlier(1993) book Correspondence Analysis in Practice, which is now in its second edition.
I read the book as someone very familiar with biplots and correspondence analysis, and onequestion I kept at the forefront of my mind was ‘what more could have been discussed (even briefly)in the book?’ My answer is ‘lots, but . . . ’. By writing the book at a very introductory level, Greenacrehas consciously focused his attention on describing the use of biplots for an audience who may not befamiliar with the topic. He has done this very well. However, there are obviously many applications notconsidered that the more learned reader may be interested in, including those from his area of expertise.While there are three chapters dedicated to biplots for correspondence analysis, there is no mention ofhow they can be used for other members of the correspondence analysis family, despite the rich andabundant literature that exists. For example, biplots were considered in the context of non-symmetricalcorrespondence analysis by Lombardo, Kroonenberg & D’Ambra (2000) and others, yet this is notmentioned. A discussion of biplots for canonical correspondence analysis is made only very briefly (pp.122–123); more on this issue can be found in Graffelman & Tuft (2004). The book also only discussesthe traditional scaling of the coordinates for a biplot, what is sometimes referred to as a symmetricbiplot . There exists a more general scaling of the generalized singular vectors that produces other typesof biplots, including isometric biplots; see, for example, Kroonenberg (2008). In fact, Kroonenberg’sbook also describes other types of biplots not considered in Biplots in Practice, such as two-modebiplots, joint biplots and nested-mode biplots.
Obviously, Biplots in Practice is not intended for those who are familiar with, or interested in,the technical rigour that sometimes accompanies such contributions to the area. Therefore, one shouldnot expect to receive an exhaustive treatment of the topics; Gower & Hand (1996), Blasius, Eilers &Gower (2009) and Gower, Lubbe & le Roux (2011), for example, do this very well. However, Biplots inPractice does provide a very good introduction to biplots and their application to a number of popularmultivariate techniques. For this reason I strongly recommend it to those wishing to learn of the practicalbenefits of biplots in multivariate statistics.
Those interested in obtaining a copy of the book can do so for free online at http://www.multivariatestatistics.org/biplots.html (correct at 7 April 2011).
BLASIUS, J., EILERS, P.H.C. & GOWER, J. (2009). Better biplots. Comput. Statist. Data Anal. 53, 3145–3158.GABRIEL, K.R. (1971). The biplot graphic display of matrices with application to principal component analysis.
GOWER, J.C. & HAND, D.J. (1996). Biplots. London: Chapman & Hall.GOWER, J., LUBBE, S.G. & LE ROUX, N. (2011). Understanding Biplots. London: Wiley.GRAFFELMAN, J. & TUFT, R. (2004). Site scores and conditional biplots in canonical correspondence analysis.
Environmetrics 15, 67–80.GREENACRE, M.J. (1993). Biplots in correspondence analysis. J. Appl. Statist. 20, 251–269.GREENACRE, M. (2009). Power transformations in correspondence analysis. Comput. Statist. Data Anal. 53,
3107–3116.GREENACRE, M. (2010). Log-ratio analysis is a limiting case of correspondence analysis. Math. Geosci. 42,
129–134.KROONENBERG, P.M. (2008). Applied Multiway Data Analysis. London: Wiley.LOMBARDO, R., KROONENBERG, P. & D’AMBRA, L. (2000). Non-symmetric correspondence analysis and
biplot representation: Comparing differences in market share distribution. J. Ital. Statist. Soc. 9(1–3),107–126.
NENADIC, O. & GREENACRE, M.J. (2007). Correspondence analysis in R, with two- and three-dimensionalgraphics: The ca package. Journal of Statistical Software 20(3), 1–13.
Analysing Seasonal Health Data. By Adrian G. Barnett and Annette J. Dobson. Springer-Verlag,Heidelberg, Dordecht, London, New York. 2010. 164 pages. £69.95 (hardback). ISBN 978-3-642-10747-4.
The preface of this book sets out the goal of detailing a wide variety of methods for investigatingseasonal patterns in disease for non-statistical researchers as well as for statisticians. A range of healthexamples are provided based on data collected daily, weekly and monthly. The authors describe theircoverage thus:
Chapter 1 introduces the statistical methods . . .. In Chapter 2, we define a ‘season’ and showsome methods for investigating and modelling a seasonal pattern. Chapter 3 is concerned withcosinor models . . .. In Chapter 4, we show a number of different methods for decomposing datato a trend, season and noise. Seasonality is not always the focus of the study; in Chapter 5, weshow a number of methods designed to control seasonality when it is an important confounder.In Chapter 6, we demonstrate the analysis of seasonal patterns that are clustered in time orspace.
Chapter 2 includes a useful introduction to various definitions of seasonality in relation to health.Annual epidemics such as flu may not be regular in timing, intensity or duration. A season is definedas ‘a pattern in a health outcome or exposure that increases and then decreases with some regularity’.There is a long-standing interest in interpreting statistical time series in biology and medicine (Cunliffe1976). My own interest arose as a result of analysis of the data of Dr. G. Charlton (pers. comm., 1989)on counts of decay, missing or filled (DMF) teeth for students of the Faculty of Dentistry, Universityof Sydney, to date of birth. Here DMF counts were strongly influenced by the student’s birth month, aseasonal effect. The effect was postulated to be related to the prenatal environment of the mother, as thesubjects were of similar age and fluoride exposure, fluoride having been introduced into the New SouthWales water supply in the 1960s and early 1970s.
The text’s methods are illustrated by application on example datasets: cardiovascular diseasedeaths (CVD – daily and monthly series, Los Angeles), schizophrenia (Australia), influenza (USA),exercise (Logan, Queensland), stillbirths (Queensland) and footballers (Australian Football League andEnglish Premier League). The CVD and schizophrenia datasets are used extensively in illustrating themethods of Chapters 3 and 4. All datasets are introduced in Chapter 1, which can be viewed online as aGoogle book extract. Many datasets are available, with supporting code for analysis, in the R package‘season’ accompanying the text. Surprisingly, little attention is drawn to the package in the text: it ismentioned in the preface, but not again. Without further reminder, considerable use is made in later
Figure 1. Monthly counts of cardiovascular disease deaths in people aged over 75 years in Los Angelesin the years 1987–2000.
chapters of commands that require the package. The package could have been identified in parenthesesor footnotes whenever its use was required.
Barnett and Dobson share a successful collaboration in explaining statistical methods in Dobsonand Barnett (2008), the third edition of Dobson’s introduction to generalized linear models. In theirlatest book they have succeeded in introducing the methods for seasonal analysis in a clear and carefulmanner. The datasets seem well chosen to illustrate the methods that are described. Emphasis is placedon testing for seasonal effects using cosinor methods (sine and cosine model terms, Chapter 3) andpresenting methods for stationary and non-stationary seasonal patterns (Chapter 4). Non-stationarymethods include a season-trend-loess (STL) decomposition, a trend model employing the Kalman filterfitted using Markov Chain Monte Carlo, models of the amplitude and phase of sinusoidal signals fittedby conditional autoregressive (CAR) Bayesian models, and random effect analyses of seasonal montheffects that are trending linearly at independent rates. In Chapter 5, methods for controlling seasonaleffects are considered. Case-crossover and matching designs are described, leading to a discussion ofadjustment for temperature estimating the effect of ozone on CVD mortality. We thus reach the importantquestion of adjusting for covariates including confounders in analysis.
Investigations of seasonal patterns may generate hypotheses about aetiology and natural history.Nevertheless, a study of seasonal disease incidence will need to be accompanied by arguments dis-tinguishing causation from association or statistical correlation (assessing the effects of confoundervariables). One of the features of some data series considered in the text is the fluctuating ampli-tude of the seasonal effect in different years. Temperature appears strongly implicated in peaks inCVD mortality (see Fig. 1) – potentially explaining the variation in amplitude of its effect in differentyears – but use of the available temperature data is not considered in the CVD mortality analysesof earlier chapters. Therefore the methods of Sections 5.1 and 5.2 are welcome additions. Finally,Chapter 6 briefly considers multiple longitudinal data series with seasonal heterogeneity and spatialmodels.
Do applications in the biological sciences differ from those in the physical sciences? Whileapplications of epidemic dynamics are largely confined to biology these models are not considered.A peculiarity of the text’s coverage is the omission of chronobiology, such as examples of diurnaland circadian rhythms, and associated statistical literature (e.g. Tong 1976), so there appears to belittle to distinguish the application areas. However, the text draws very little on traditional time seriesmethods; rather, its approach appears to draw heavily on methods for longitudinal data analysis. Do thetraditional methods still provide insights for the datasets considered here? While the autocorrelationfunction is introduced, there is no consideration of reducing non-stationarity through differencing, norof the introduction of harmonics of sinusoidal terms to provide finer-scale modelling of the series, asmight appear suitable when fitting sharp or secondary peaks (see fig. 4.25) or sawtooth seasonal patterns(Chapter 3.3) and other ‘non-sinusoidal’ behaviour. In fact, there are no references to traditional appliedtime series texts (e.g. Bloomfield 1976; Brillinger 1975, and later texts) other than Chatfield’s.
The study design and variables of the significant datasets, particularly CVD and schizophrenia,are not well described. The reference to the CVD dataset is an inaccessible US technical report, whilethe schizophrenia study appears to be a retrospective study following diagnosis, but no details areprovided of its design. If the study is retrospective, are we identifying the full target population orselectively excluding more recent births? Does not analysis or interpretation dependent on aspect of thedesign: whether the outcomes measure incidence or prevalence, whether the study is retrospective orprospective? The lack of detail could be corrected in the package ‘season’.
Both book, in Chapter 4, and R package, in ‘examples()’ scripts, are incomplete in detailing thespecifics of how one would implement the more advanced analyses described in Chapter 4 (code isprovided for stationary cosinor modelling and STL decompositions). The incompleteness is unfortunate,as the methods are complex and analyses appear difficult to reproduce. The authors appear to haveincluded, in Chapter 4 and Chapter 5.2, methods found useful in their own research. The use andunderstanding of these methods would be enhanced by the availability of code.
Summing up, the authors are to be commended on a useful and clear introduction to seasonal healthdata analysis. The text will be helpful to statisticians, particularly in combination with the associated Rpackage ‘season’, which will encourage them to test their own preferred methods in context and assist inteaching seasonal modelling. Non-statistical researchers may find the advanced methods tough-going,and would benefit from reviewing other time series approaches to seasonal data analysis.
MALCOLM HUDSON
Department of Statistics, Macquarie University,Faculty of Medicine, University of Sydney
BLOOMFIELD, P. (1976). Fourier Analysis of Time Series: An Introduction. New York: Wiley.BRILLINGER, D.R. (1975). Time Series: Data Analysis and Theory. New York: Holt, Rinehart and Winston.CUNLIFFE, S.V. (1976). Interaction. J. Roy. Statist. Soc. Ser. A 139, 1–19.DOBSON, A. & BARNETT, A. (2008). An Introduction to Generalized Linear Models. Florida: CRC Press.TONG, Y.L. (1976). Parameter estimation in studying circadian rhythms. Biometrics 32, 85–94.
Linear Causal Modeling with Structural Equations. By Stanley Mulaik. Boca Raton, FLChapman & Hall/CRC, 2009. 468 pages. £50.99 (hardback). ISBN 978-1-4398-0038-6.
The book is written by one of the most prominent researchers in the field of structural equation models(SEM). It is a part of the ‘Statistics in the Social and Behavioral Sciences Series’ by Chapman &Hall/CRC and, as such, it is focused on recent developments in statistical methodology in social and
behavioural sciences. It is primarily a useful textbook for graduate students but could also be veryuseful for researchers in quantitative methods. The new topics that ‘got me hooked’ were related mainlyto the extended philosophical treatment of causality. The author’s main point is that causation is bestunderstood as a functional relation between variables. After an extensive review of the perception ofcausation in the works of David Hume, J.J. Gibson, C.R. Twardy and G.P. Bingham, P. Wolff, andmost notably G. Lakoff and M. Johnson, he presents his own conception of probabilistic causalityand its modelling with functional relations between variables. It becomes simple to understand prob-abilistic causality as a functional relation between two sets: the first set (the domain) containing thevalues of the causal variable, and the second set (the range) containing as its elements the probabilitydistributions defined on the dependent variable. His rigorous definition puts into context many earlierdevelopments and causality models. In particular, the standard local independence assumption turnsout to be a necessary and sufficient condition for probabilistic causality. He also reviews recent ad-vances in counterfactual analysis, graphical models and nonparametric structural equations in light ofhis definition. As an upshot, the book presents the standard methods of SEM in a form that makes theminteresting to students and researchers with interests in the philosophical treatment of causality usingSEM.
The author states in the preface that some sections of the book are mathematically challenginggiven the nature of the main audience for his book. Personally, having reviewed other books on SEM, Ithink that he strikes the right balance, and the introductory chapter containing preliminaries from linearalgebra prepares the reader for any mathematical challenges ahead. This is followed by a ‘philosophical’chapter about causality and a discussion on probabilistic causality. Next, the author turns to presentingthe basics of structural equation theory. His presentation here is sequential, starting with a descriptionof the relationships in an equation form, then giving them in a path diagram form, and finally in a matrixform. Chapter 6 is devoted to identification rules and the discussion of equivalent models in SEM.Methodologically, the presentation is nicely led and illustrated with the simple confirmatory analysisfactor model. Personally, I think this chapter could have been more thorough and up-to-date, given theimportance of the identification rules in SEM models. Chapter 7 is devoted to parameter estimationin SEM. The discussion here is thorough and includes the relatively involved asymptotic distributionfree estimation methods of Michael Brown. The level of mathematical sophistication and detail inthis chapter stands out in comparison to that of the remaining chapters, and some details may not beinteresting for the typical reader of the book. I also noticed more misprints in this chapter, althoughfortunately none of them is truly egregious.
The remainder of the book (Chapters 8–16) treats more specific issues in SEM, such as designingSEM studies, the use of instrumental variables to resolve issues of causal direction, multilevel andlongitudinal models in SEM, and the use of polychoric and polyserial correlation. I was happy to see aseparate chapter on the issue of equivalent models (Chapter 10). The latter models often occur in largenumbers in SEM and may entail different and sometimes incompatible or even opposite explanationsof the studied phenomena. This is why they deserve a place in a book with applied orientation, such asthe current text. Thorough discussion of equivalence is very welcome in this particular book, as it isdevoted to linear causal modelling using SEM. The issue of how to exclude equivalent models in favourof a given model using causality arguments becomes central. The author’s suggestion of consideringtemporal ordering among the variables to make the decision is very appropriate.
Towards the end of the book, in Chapter 14, non-recursive models are considered. The discussionhere mainly follows the material in Heise’s (1975) Causal Analysis.
Chapter 15 deals with model evaluation. This is the longest chapter. It covers in detail chi-squareand corrected chi-square statistics, and the variety of goodness-of-fit indices used in SEM. Many of thetopics here are closely related to the author’s own contributions to the field. I find this particular chapterto be very well written. It discusses the philosophy behind model evaluation and the logical sequenceof steps to follow in order to test the assumptions and the constraints of the model. It is well known thatgoodness-of-fit indices have divided researchers in SEM into two camps: those who embrace them andthose who heavily criticize them. Mulaik finishes Chapter 15 by entering this discussion and presentinghis point of view. He seeks the middle ground between the two camps and argues convincingly that the
complexity of the hypothesized models in SEM necessitates that both types of indices (the chi-squaretest and the approximate indices) can and should be used in model evaluation.
In conclusion, this is a very useful textbook for graduate students. It stands out for its rigoroustreatment of SEM as a whole and for a particularly useful philosophical treatment of causality. Partly asa result of the availability of computer packages such as LISREL, EQS and MPLUS, among others, SEMis a rapidly developing field, and many new textbooks and monographs appear every year. However,Stanley Mulaik’s book is one of the most useful ones with which to start a journey in this field.
WOLFF, P. (2007). Representing causation. Journal of Experimental Psychology 136, 82–111.
Statistical Image Processing and Multidimensional Modeling. By Paul Fieguth. New York, NY:Springer. 2010. pages. €79.95 (hardback). ISBN 978-1-4419-7293-4.
This text by Paul Fieguth is concerned with statistical image processing. Statistical image processingdiffers from the more generic imaging processing techniques found in electrical engineering: whereasgeneral image processing deals with images that may not be well described by a statistical or mathemat-ical model, statistical image processing seeks to exploit such a model to address questions in fields suchas remote sensing, medical imaging and computer vision, and other high-dimensional spatial problems.There is some overlap between the two approaches, including topics such as de-noising and image seg-mentation, but even in discussion of these procedures the pervasive emphasis is on modelling. The datasets to be modelled are often more correctly classified as multidimensional spatial data sets, rather thanimages, with one or more measurements taken over a two- or higher-dimensional space (for example,the temporal interpolation of ocean temperature). In these cases standard image processing algorithmsmay not apply.
The scope of the book is wide, and it contains intriguing examples from many fields. The statedgoal of the text is to avoid being either entirely mathematical/theoretical or entirely applied/algorithmic.It benefits from strong organization, so the variety of subject matter is not overwhelming. The maincontent of the book is structured in three parts. Part I develops the basic theory of inverse problemsand estimation – including both Bayesian and non-Bayesian approaches – and covers both static anddynamic estimation and sampling. Part II covers the mathematical modelling of random fields, includingmultidimensional modelling, Markov random fields, hidden Markov models, fast Fourier transformmethods, and wavelet approaches. Part III is concerned with algorithms and numerical methods forsolving a given problem. The book also contains a useful Appendix giving brief background materialon matrix algebra, basic statistics, and standard image processing techniques.
The book would be an excellent reference book for a statistician or engineer with interests inimage processing. It would also make a fine text for a graduate class, despite there being only a smallnumber of problems at the end of each chapter, and no corresponding solutions. Statisticians may findsome the notation slightly non-standard (e.g. m for measurements rather than x for data); however, thenotation is well defined and set out so any confusion is readily resolved. An innovative feature of the
references section is that, in addition to an alphabetical list, it provides lists of papers by topic and incategories such as ‘Classic papers’ and ‘Highly cited papers’.
There is no code in the book itself, although some algorithms are represented in pseudo-code.There is an author website, which contains some extra supporting material, including colour figures(unfortunately the book contains no colour figures) and sample Matlab scripts. Unfortunately, at thetime of writing several of the links to the Matlab code were not working.
Overall this book is an excellent overview of the subject, successfully bridging the gap betweenthe fields of statistics and engineering. It explores algorithms and applications, but all the time with anunderlying modelling ethos.
