Characteristically, exploratory data analysis (chapter 2) precedes the introduction of the random function (chapter 3). The chapter on inference and modeling of a multivariate model (chapter 4) is, in my opinion, the best ever written on the subject. Pierre could have been bolder by giving precedence to uncertainly assessment over estimation, but he chose to present first the estimation tools (chapters 5 and 6). this is the most complete yet cohesive exposé of all the various flavors of kriging and cokriging. The emphasis is not on the illusory kriging variance but rather on building estimators that can account for the large diversity of information types characteristic of earth sciences. The very reason for geostatistics and the future of the discipline lie in the modeling of uncertainly, at each node through conditional distributions (chapter 7) and globally through stochastic images (conditional simulations, chapter 8). In modern geostatistics, which is driven by conditional simulations, kriging is an engine, and not the only one, to build models of conditional probability distribution. Kriging estimates and kriging variances have lost their original luster: the former because of their uneven smoothing and the latter because of their data independence. The practice of geostatistics has always been ahead of academic publications. This book finally may have caught up with the use of random function model in the earth sciences, but geostatistics has already freed itself from the frame of such models. It befits that the door of an era be closed by a mean of the future. The main text of the book is divided into seven chapters, covering the most important areas of geostatistical methodology. The presentation follows the typical steps of a geostatistical analysis, introducing tools for description, quantitative modeling of spatial continuity, spatial prediction and uncertainty assessment. To facilitate reading and as an attempt at standardization, this book uses the notation of the GSLIB guidebook. The various tools are illustrated using a multivariate soil data set related to heavy metal contamination of a 14.5 km2 region in the Swiss Jura. The geostatistical analysis was carried out using the GSLIB software. Although this data set gives the book a definite environmental flavor, presentation of the algorithms is general and intended for students and practitioners desiring to gain an understanding of the methodology. Mathematical developments underlying most interpolation algorithms are given; therefore, the reader should have some prior notions of linear algebra, in addition to an undergraduate knowledge of statistics. These theoretical developments may be skipped, however, on first reading, without altering comprehension of the case studies.
