Statistical analysis of spatial point patterns.

*(English)*Zbl 0559.62088
Mathematics in Biology. London - New York etc.: Academic Press. A Subsidiary of Harcourt Brace Jovanovich, Publishers. IX, 148 p. $ 25.00 (1983).

A spatial point pattern is a set of locations, irregularly distributed within a region of interest, which have been generated by some unknown random mechanism. Such kind of data in the form of a set of points, irregularly distributed within a region of space, arise in many different biological contexts. Such data set is called a ”spatial point pattern”. In this book, an up-to-date account of statistical methods for analysing spatial point patterns, in a style which is accessible to numerous biologists as well as to statisticians is given.

The first three chapters ”Introduction”, ”Preliminary testing for mapped patterns” and ”Analysis of sparsely sampled patterns” deal mainly with tests of randomness and are intended as a self-contained and mathematically elementary introduction. Chapter 4 ”Spatial point processes” and Chapter 5 ”Analysis of mapped patterns” cover the formulation and fitting of stochastic models for spatial point patterns. Chapter 6 ”Multivariate spatial point processes” and Chapter 7 ”Analysis of multivariate patterns” extend the discussion to patterns in which the locations are of several distinguishable types.

All the methods are illustrated using real biological data sets, which are presented in full as an Appendix. It is assumed throughout that the reader’s knowledge of statistics includes elementary probability theory and the basic principles of parameter estimation and hypothesis testing. Most of the methods of analysis require a computer for their implementation and computational aspects are discussed as they arise. The important approach taken in this excellent book is to develop methods for the analysis of spatial patterns based on stochastic models. Similar problems arise in many other disciplines, like archaeology, astronomy and geography.

The first three chapters ”Introduction”, ”Preliminary testing for mapped patterns” and ”Analysis of sparsely sampled patterns” deal mainly with tests of randomness and are intended as a self-contained and mathematically elementary introduction. Chapter 4 ”Spatial point processes” and Chapter 5 ”Analysis of mapped patterns” cover the formulation and fitting of stochastic models for spatial point patterns. Chapter 6 ”Multivariate spatial point processes” and Chapter 7 ”Analysis of multivariate patterns” extend the discussion to patterns in which the locations are of several distinguishable types.

All the methods are illustrated using real biological data sets, which are presented in full as an Appendix. It is assumed throughout that the reader’s knowledge of statistics includes elementary probability theory and the basic principles of parameter estimation and hypothesis testing. Most of the methods of analysis require a computer for their implementation and computational aspects are discussed as they arise. The important approach taken in this excellent book is to develop methods for the analysis of spatial patterns based on stochastic models. Similar problems arise in many other disciplines, like archaeology, astronomy and geography.

Reviewer: T.Postelnicu

##### MSC:

62P10 | Applications of statistics to biology and medical sciences; meta analysis |

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

65C99 | Probabilistic methods, stochastic differential equations |

62M99 | Inference from stochastic processes |

62Pxx | Applications of statistics |