Page 9 - Applied Probability

Preface to the First Edition
When I was a postdoctoral fellow at UCLA more than two decades ago,
I learned genetic modeling from the delightful texts of Elandt-Johnson [2]
and Cavalli-Sforza and Bodmer [1]. In teaching my own genetics course over
the past few years, first at UCLA and later at the University of Michigan,
I longed for an updated version of these books. Neither appeared and I was
left to my own devices. As my hastily assembled notes gradually acquired
more polish, it occurred to me that they might fill a useful niche. Research
in mathematical and statistical genetics has been proceeding at such a
breathless pace that the best minds in the field would rather create new
theories than take time to codify the old. It is also far more profitable to
write another grant proposal. Needless to say, this state of affairs is not
ideal for students, who are forced to learn by wading unguided into the
confusing swamp of the current scientific literature.
Having set the stage for nobly rescuing a generation of students, let me
inject a note of honesty. This book is not the monumental synthesis of pop-
ulation genetics and genetic epidemiology achieved by Cavalli-Sforza and
Bodmer. It is also not the sustained integration of statistics and genetics
achieved by Elandt-Johnson. It is not even a compendium of recommen-
dations for carrying out a genetic study, useful as that may be. My goal
is different and more modest. I simply wish to equip students already so-
phisticated in mathematics and statistics to engage in genetic modeling.
These are the individuals capable of creating new models and methods
for analyzing genetic data. No amount of expertise in genetics can over-
come mathematical and statistical deficits. Conversely, no mathematician
or statistician ignorant of the basic principles of genetics can ever hope to
identify worthy problems. Collaborations between geneticists on one side
and mathematicians and statisticians on the other can work, but it takes
patience and a willingness to learn a foreign vocabulary.
So what are my expectations of readers and students? This is a hard
question to answer, in part because the level of the mathematics required
builds as the book progresses. At a minimum, readers should be familiar
with notions of theoretical statistics such as likelihood and Bayes’ theorem.
Calculus and linear algebra are used throughout. The last few chapters
make fairly heavy demands on skills in theoretical probability and combi-
natorics. For a few subjects such as continuous time Markov chains and
Poisson approximation, I sketch enough of the theory to make the expo-
sition of applications self-contained. Exposure to interesting applications
should whet students’ appetites for self-study of the underlying mathemat-