Traditionally, applied probability texts contain a fair amount of probability
theory, varying amounts of applications, and no data.
Occasionally an author may touch upon how one would go
about fitting a model to data, or use data to develop a model,
but rarely is this topic given much weight.
On the other hand,
the few texts on inference for stochastic processes mostly dwell at length
upon the interesting twists that occur in statistical theory when data no longer
can be assumed iid. But, again, they rarely contain any data. The intent of this
text is to present some probability models, some statistics relevant to these
models, and some data that illustrate some of the points made.

My experience as a practicing statistician, specializing in models for dependent
data, has been that no real progress can be made without spending substantial
time trying to master enough of the subject matter to be able to talk to area
scientists in their language, rather than in mathematical language. Consequently,
I have tried to give scientific background to many of the applications I
present in more detail than is usual in statistics texts. A general
scientific background, but no special training, should suffice to enable you
to follow the gist of the explanations. From a mathematical point of view you
need elementary probability, including conditional distributions and
expectations, calculus, ordinary differential equations, and linear
algebra. Having encountered statistics would be very useful, although it is
not strictly necessary. My students tell me that a first course in stochastic
processes is a very useful background, but I have tried to include sufficient
material to make this unnecessary.
I avoid measure-theoretical arguments, but have to
use some L
-theory to introduce (albeit in an extremely low-key
manner) stochastic integration.` `

As the chapters progress, there are fewer formal proofs and more
references to the literature for verification of results. This is because while
it is possible to do much discrete time Markov chain theory using elementary
probability, it becomes progressively harder to do the proofs as the
processes become more complicated. I therefore often resort to special cases
and intuitive explanations in many instances.` `

Picking topics is necessarily a very subjective matter. I have omitted some
topics that others
may find essential. For example, while renewal theory is
a beautiful piece of probability, I have not found many interesting
scientific applications. Martingales are not included, in spite of their
usefulness in statistical theory. I ignore stationary time series, since in
this area there are plenty of books containing both theory and data analysis.` `
On the other hand I try to emphasize the
importance of Markov chain Monte Carlo methods, which are having as profound
an impact on statistics in the nineties as did the bootstrap in the eighties.` `
I have found the state space modeling approach useful in a variety of
situations, as I am sure you can tell.` `

At first I was intending to write a short introduction, indicating why I think
stochastic models are useful. It grew into a chapter of its own.` `
Three appendices contain some
material that not everyone may have encountered before. I hope there is
enough so that, for example, someone without much mathematical statistics
will get an idea of the main tools (that will be used in the text).` `

The material in this book is suitable for a two-semester course. I have tried
to cover most of it in a two-quarter sequence, but that gets a bit rushed.
When I teach this course, one of the main teaching tools is laboratory
assignments, where the students work on analyzing data sets, simulating
processes and statistical procedures, and work through some theory as
well. I have included versions of these laboratory assignments in the
exercises that follow each chapter. These exercises contain extensions and
details of the probabilistic exposition, computational exercises, and data
analysis problems. In conjunction with the book, several data sets will
be available via anonymous ftp (details are given after the indexes).` `

There is a variety of examples and applications. The former are attempts to
illustrate some concepts while the latter apply the concepts to
data.` `
In order to facilitate reference to the book in lectures I have numbered all
displayed equations. Theorems,
propositions, lemmata, figures, and tables are separately numbered.` `
To simplify life a little for the readers there
are, in addition to the regular indexes of terms and notation,
indexes of examples/applications
and of numbered theorems, propositions, and lemmata.
Definitions are indicated with bold typeface
(and referred to in the Index of terms). As is common in applied probability
(but not in statistics),
all vectors are row vectors.` `

The applications in the text draw on many different sources. Some originate in
work by me or my students, others come from colleagues and friends who I have
talked into giving me their data, and yet others are quoted from the
literature. At the end of each chapter I try to acknowledge my main sources, as
well as give occasional hints as to where one can learn more (preferably
discussion papers). I
apologize for any inadvertent failures to make such acknowledgements.` `

A large number of students and colleagues have had comments and suggestions
regarding the text. Julian Besag, Michael Phelan, and Elizabeth Thompson have been particularly
helpful, as well as a host of students over the years. Four reviewers made
numerous helpful comments: Simon Tavare, Michael P. Bailey, David D. Yao
and Laurence Baxter. John Kimmel was a patient and helpful editor throughout
the project, while Achi Dosanjh and Emma Broomby skillfully guided me through
the final stages of manuscript preparation.` `
Several colleagues have generously provided data, figures or other help.` `
I would particularly
like to thank
Joao Batista,
David Brillinger,
Anna Guttorp,
David Higdon,
Jim Hughes,
Stephen Kaluzny,
Niels Keiding,
Brian Leroux,
Hongzhe Li,
Iain MacDonald,
Roland Madden,
Thomas Murray,
Michael Newton,
Haiganoush Preisler,
John Rice,
Brian Ripley,
Nuala Sheehan,
Jim Smith, and
Elizabeth Thompson.` `

The text was produced using Eroff from Elan Computer Group, Inc.` `
The statistical analysis was generally done in Splus (StatSci
division of Mathsoft, Inc.)
and most figures benefited
greatly from the psfig utility written by Antonio Possolo and the setps
wrapper written by Frank Harrell. The spatial
point process analysis employed the Splancs library produced by
B. S. Rowlingson and Peter Diggle at Lancaster University. Software for
some specialized analyses was provided by Charlie Geyer and John Rice.` `

This work had partial support from the National Science Foundation (DMS-9115756),
the National Institute of Health (HL 31823), the Environmental Protection Agency,
and the Electrical Power Research Institute. This text cannot in any way be
construed as official policy of any of these organizations. The final version
was produced during a visiting scholar appointment at the Institute for
Environmental Studies at the University of Washington, and I am grateful
for their generous support during a most difficult time.` `

My family has patiently suffered through my long preoccupation with this
manuscript. June, Eric, and Kenji deserve much more attention (and will,
hopefully, get it) from me. They have been very supportive of the effort.` `

I was fortunate to have Jerzy Neyman and David Brillinger as advisers when I was a graduate student. From them I learned a way of thinking about science, about data, and about modeling. And I learned, in Mr. Neyman's words, that ``Life is complicated, but not uninteresting.''