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Review of

PRACTICAL GEOSTATISTICS 2000 by Isobel Clark and William V. Harper, Columbus, OH: Ecosse North America Llc, 2000, ISBN 0-9703317-0-3, 342 pp., $60.00.

As noted by the authors, this book is an update of an earlier version in 1979, the principal changes pertain to the addition of material providing a more classical statistics background.

There are a total of twelve chapters, a bibliography, a collection of statistics tables, hard copies of the various data sets used in the discussions and an index. Following the Preface, there is a two page list of notations. See later comments for errors in this listing.

Chapter One describes the intended audience, provides a brief overview of the data sets that will be used and refers to the software used in the book. The software is a simpler version of a commercial package produced by I. Clark's consulting company, a demo version of the software can be downloaded from the main kriging web site. The reader might be better advised to get a free copy of the GEOEAS software which can be downloaded from the www.ai-geostats.org website.

Chapter Two reviews basic descriptive statistics. Four data sets are used for illustration. Chapter Three reviews some of the basic properties of the Normal Distribution. Chapter Four reviews the lognormal and three-parameter lognormal distributions. Chapter Five is a very short review of the Binomial, Negative Binomial, Geometric, Poisson and Compound Poisson distributions. Chapter Six reviews the basics of hypothesis testing; mean, standard deviation, difference of two means. Chapter Seven introduces regression and Trend Surfaces.

Chapter Eight is the first instance of a discussion of spatial data. Chapter Nine describes the estimation and modeling of variograms. Chapter Ten introduces Ordinary kriging. Chapter Eleven extends the point kriging in the previous chapter to block kriging, i.e., estimation of averages over areas or volumes. Chapter Thirteen is a very brief discussion of lognormal kriging, kriging in the presence of a non-stationarity, Indicator kriging and rank transform kriging.

The strongest point in the book is the consistent use, of several data sets, throughout the book. The weak point is the presence of many errors.

The authors claim that the book is intended for beginners and in particular those without a strong mathematical background. In fact there is a lot of mathematics in the book, although it is mostly trivial such as algebraic simplification of the formula for a sample variance. The reader need not be burdened with a lot of the mathematical details, e.g., derivations, but at the same time authors should avoid saying things that are incorrect. If a result is to be motivated by heuristics then it should be clearly labeled as such. There are a great many errors in the chapters on statistics and many in those on geostatistics as well. The discussion of confidence intervals is mostly incorrect. It is claimed at one point that a variogram must be "conditionally positive definite", in fact it is the negative of the variogram that must be conditionally positive definite, i.e., the variogram must be conditionally negative definite. The discussion of the nugget effect has a number of mistakes, the authors do not properly distinguish between the variogram being non-zero at the origin and having a jump discontinuity. They do not distinguish between kriging with a variogram having a non-zero nugget and the variation of kriging which results in smoothing, e.g., the thin plate spline vs the smoothing spline.

In the list of notations, e is identified as the natural anti-log function. In the preface, 2x is incorrectly identified as the differential of x2, rather than as the derivative. χ is identified as the "distribution of sample variances from Normal samples" (not even χ2 but χ ). μ is identified as the "arithmetic mean of values in a Normal population". In several places it simply denotes the expected value of a random variable (not necessarily Normal). In Chapter 2 it is claimed that the sample standard deviation (of a set of heights) can be interpreted as "the typical difference between the actual height of any class member and the average height of the class". The kurtosis is defined as the fourth central moment which can then be standardized by the square of the variance (italics added for emphasis)

The book is fraught with strange phrases. "For one thing it can not go negative-there is no such thing as a negative probability" (speaking of probability density functions). "Many distribution functions have strange looking constants in the formula, simply to ensure that the area under the curve is 1". "In particular, the Normal distribution is the only one which is always the same shape". "Statistical theory can show us what this new population will look like". "We find a 90% confidence interval is contained by the Student's t value of, so that" (italics added for emphasis). The t-statistic is incorrectly defined on page 44 (the _n is missing).

In summary, a knowledgeable reader will find some interesting examples and will be able to steer around the mis-statements. It is not recommended for a beginner since they will likely not recognize the mistakes.

 

Donald E. Myers

Department of Mathematics

University of Arizona

Tucson, AZ 85721

myers@math.arizona.edu

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