##
**Multivariate geostatistics. An introduction with applications.
2nd completely rev. ed.**
*(English)*
Zbl 0912.62131

Berlin: Springer. xiv, 291 p. (1998).

[For the review of the first edition from 1995 see Zbl 0871.62105.]

This book presents an introduction to geostatistics from a multivariate perspective. The material is subdivided into five parts. Part A reviews the basic concepts of mean, variance, covariance, mathematical expectation, linear regression and multiple linear regression. The problem of estimating the mean of spatially or temporally correlated data is solved by kriging. Part B offers a detailed introduction to linear geostatistics for a single variable. After presenting the random function model and the concept of stationarity, the display of spatial variations with a cloud variogram is discussed. Special attention is paid to variograms and their theoretical properties. Part C presents three well-known methods of multivariate analysis; namely principal components method, canonical analysis and correspondence analysis. Part D extends linear geostatistics to the multivariate case. The properties of the cross variogram and the cross covariance function are discussed and compared. Two models, the intrinsic correlation model and the nested multivariate model, are examined in the light of two multivariate random function models, the linear and bilinear coregionalization models. Finally, part E discusses phenomena involving a non-stationary component called the drift. The Appendix contains some reminders on linear algebra and linear regression theory as well as a list of common covariance functions and variograms. Applications from different areas of science and exercises are integrated into the text.

This book is intended for scientists, engineers or statisticians who are interested in methods and techniques for the analysis, estimation and display of multivariate data distributed in space or time.

This book presents an introduction to geostatistics from a multivariate perspective. The material is subdivided into five parts. Part A reviews the basic concepts of mean, variance, covariance, mathematical expectation, linear regression and multiple linear regression. The problem of estimating the mean of spatially or temporally correlated data is solved by kriging. Part B offers a detailed introduction to linear geostatistics for a single variable. After presenting the random function model and the concept of stationarity, the display of spatial variations with a cloud variogram is discussed. Special attention is paid to variograms and their theoretical properties. Part C presents three well-known methods of multivariate analysis; namely principal components method, canonical analysis and correspondence analysis. Part D extends linear geostatistics to the multivariate case. The properties of the cross variogram and the cross covariance function are discussed and compared. Two models, the intrinsic correlation model and the nested multivariate model, are examined in the light of two multivariate random function models, the linear and bilinear coregionalization models. Finally, part E discusses phenomena involving a non-stationary component called the drift. The Appendix contains some reminders on linear algebra and linear regression theory as well as a list of common covariance functions and variograms. Applications from different areas of science and exercises are integrated into the text.

This book is intended for scientists, engineers or statisticians who are interested in methods and techniques for the analysis, estimation and display of multivariate data distributed in space or time.

Reviewer: Ivan Křivý (Ostrava)

### MSC:

62P99 | Applications of statistics |

86A32 | Geostatistics |

62H25 | Factor analysis and principal components; correspondence analysis |

86-01 | Introductory exposition (textbooks, tutorial papers, etc.) pertaining to geophysics |

62-01 | Introductory exposition (textbooks, tutorial papers, etc.) pertaining to statistics |

00A06 | Mathematics for nonmathematicians (engineering, social sciences, etc.) |