## Statistics for spatio-temporal data [book review]

**H**ere is the new reference book about spatial and spatio-temporal statistical modelling! Noel Cressie wrote the earlier classic *Statistics for Spatial Data* in 1993 and he has now co-authored with Christopher Wikle (a plenary speaker at ISBA 2014 in Cancún) the new bible on the topic. And with a very nice cover of a Guatemaltec *lienzo* about the Spanish conquest. *(Disclaimer: as I am a good friend of Noel, do not expect this review to remain unbiased!)*

“…we state the obvious, that political boundaries cannot hold back a one-meter rise in sea level; our environment is ultimately a global resource and its stewardship is an international responsibility.” (p.11)

**T**he book is a sum (in the French/Latin meaning of *somme/summa* when applied to books*—I am not sure this explanation makes any sense!*) and, as its predecessor, it covers an enormous range of topics and methods. So do not expect a textbook coverage of most notions and prepare to read further articles referenced in the text. One of the many differences with the earlier book is that MCMC appears from the start as a stepping stone that is necessary to handle

“…there are model-selection criteria that could be invoked (e.g., AIC, BIC, DIC, etc.), which concentrate on the twin pillars ofpredictabilityandparsimony. But they do not address the third pillar, namelyscientific interpretability(i.e., knowledge).” (p.33)

**T**he first chapter of the book is actually a preface motivating the topics covered by the book, which may be confusing on a first read, esp. for a graduate student, as there is no math formula and no model introduced at this stage. Anyway, this is not really a book made for a linear read. It is quite witty (with too many quotes to report here!) and often funny (I learned for instance that Einstein’s quote *“Everything should be made as simple as possible, but not simpler”* was a paraphrase of an earlier lecture, invented by the *Reader’s Digest*!).

“Thus, we believe that it is not helpful to try to classify probability distributions that determine the statistical models, as subjective or objective. Better questions to ask are about the sensitivity of inferences to model choices and whether such choices make sense scientifically.” (p.32)

**T**he overall tone of the book is mostly Bayesian, in a non-conflictual conditional probability way, insisting on hierarchical (Bayesian) model building. Incidentally, it uses the same bracket notation for generic distributions (densities) as in Gelfand and Smith (JASA, 1990), i.e. [X|Y] and [X|Z,y][Z|y,θ], notation that did not get much of a fan club. (I actually do not know where it stemmed from.) The second chapter contains an illustration of the search for the USS Scorpion using a Bayesian model (including priors built from experts’ opinions), example which is also covered [without the maths!] in Sharon McGrayne’s Theory that would not die.

**T**he book is too rich and my time is too tight (!) to cover each chapter in details. (For instance, I am not so happy with the temporal chapter in that it moves away from the Bayesian perspective without much of a justification.) Suffice to say then that it appears like an updated and improved version of its predecessor, with 45 pages of references, some of them quite recent. If I was to teach from this book at a Master level, it would take the whole academic year and then some, assuming enough mathematical culture from the student audience.

**A**s an addendum, I noticed several negative reviews on amazon due to the poor quality of the printing, but the copy I received from John Wiley was quite fine, with the many colour graphs well-rendered. Maybe an earlier printing or a different printing agreement?

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