Page 20 - Computational Statistics Handbook with MATLAB

Chapter 1: Introduction 5

We conclude the book with a chapter on spatial statistics as a way of show-
ing how some of the methods can be employed in the analysis of spatial data.
We provide some background on the different types of spatial data analysis,
but we concentrate on spatial point patterns only. We apply kernel density
estimation, exploratory data analysis, and simulation-based hypothesis test-
ing to the investigation of spatial point processes.
We also include several appendices to aid the reader. Appendix A contains
a brief introduction to MATLAB, which should help readers understand the
code in the examples and exercises. Appendix B is an index to notation, with
definitions and references to where it is used in the text. Appendices C and D
include some further information about projection pursuit and MATLAB
source code that is too lengthy for the body of the text. In Appendices E and
F, we provide a list of the functions that are contained in the MATLAB Statis-
tics Toolbox and the Computational Statistics Toolbox, respectively. Finally,
in Appendix G, we include a brief description of the data sets that are men-
tioned in the book.

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The explanation of the algorithms in computational statistics (and the under-
standing of them!) depends a lot on notation. In most instances, we follow the
notation that is used in the literature for the corresponding method. Rather
than try to have unique symbols throughout the book, we think it is more
important to be faithful to the convention to facilitate understanding of the
theory and to make it easier for readers to make the connection between the
theory and the text. Because of this, the same symbols might be used in sev-
eral places.
In general, we try to stay with the convention that random variables are
capital letters, whereas small letters refer to realizations of random variables.
For example, X is a random variable, and x is an observed value of that ran-
dom variable. When we use the term log, we are referring to the natural log-
arithm.
A symbol that is in bold refers to an array. Arrays can be row vectors, col-
umn vectors or matrices. Typically, a matrix is represented by a bold capital
letter such as B, while a vector is denoted by a bold lowercase letter such as
b. When we are using explicit matrix notation, then we specify the dimen-
sions of the arrays. Otherwise, we do not hold to the convention that a vector
always has to be in a column format. For example, we might represent a vec-
(
,
,
tor of observed random variables as x 1 x 2 x 3 ) or a vector of parameters as
,
( µσ) .

© 2002 by Chapman & Hall/CRC