Mathematical-tools

As a substitue, I recommend Gelman et al. Bayesian data analysis which treats the same topics but is much more clear and better explained as well as more modern.
I got this book since this was a text book for a class, but ended up using other books (like Gleman's).

The orientation is toward the Bayesian approach however, with good coverage of prior and posterior distributions, conjugate priors and Bayesian Hierarchical Models. The last chapter on Markov Chain Monte Carlo methods is mostly used for Bayesian inference.

This is a great reference source but can also be used in a graduate level course on mathematical statistics, probably as a supplemental text. There are many useful exercises in this edition. The book is fairly advanced and presupposes an introduction to mathematical statistics at the level of the text by Bickel and Doksum. It also assumes that the reader has had some introduction to Bayesian methods but only at the level of, say, Box and Tiao's text. It does not assume any knowledge of stochastic processes including Markov chains.

Convergence properties for the Markov Chain Monte Carlo algorithms (MCMC) are crucial to their success. Elements of discrete Markov chains are introduced in chapter 6 to make the algorithms understandable, but proof of convergence are avoided because they would involve a more detailed account of Markov chain theory.

Tanner provides a good list of the references that were available in 1996. The research in MCMC methods is continuing to be intense and so there are many good references that have appeared since the publication of this book. Robert and Casella (1999) provides a more detailed and more current treatment but even that book is a couple of years dated.

The EM and data augmentation algorthms are used for problems that are classified as missing data problems. The data may be missing as in a survey where particular questions are not answered by the respondents or it could be censored data as in a medical study or clinical trial. The censored data problem is illustrated by Tanner using the Stanford Heart Transplant data. Mixture models are also handled via these algorithms since the identification of the component that the observation belongs to can be viewed as missing data.

Tanner demonstrates a wide variety of techniques to handle many important problems and he illustrates them on real data. It is nice to have all of this compactly written in just 200 pages!

The main part of this book is focused on methods of how to value american vanilla options. He does this only in the diffusion transformed version of B&S. He starts with the equation in this form, without mentioning much of how to get there, and why. And thats typical for the rest of the book aswell, much of it is "cookery book form" (even if the book contains lots of usefull references in the endchapter). He discusses several ways of solving PDE:s, mainly implicit/explicit/Crank N and then there is a very introductory chapter on FEM. The discussion on stability issues is to brief (and not to understandable), I'd say (Tavella does this much more elegant). In the endchapter he discusses how to value exotic options (using asian as a case), and concludes that the methods ealier in the book isnt of much use, but as the author says this is an introductory book.

CHAPTER 1: SCIENTIFIC REVOLUTION
Dyson revisits scientific disciplines that have come about as a result of brilliant minds exploring a previously unexisting path of research. In doing so, he makes an effort to extrapolate out of today's most rapidly growing areas of science (molecular biology and astronomy) what the future scientific revolutions might be like, and gives wise words of advise to medical scientists and biologists on how to make faster progress in their disciplines by changing some of their fundamental research paradigms, learning from the ways of astronomers.

CHAPTER 2: TECHNOLOGY AND SOCIAL JUSTICE
In more than one way, it reminds me of a very pivotal article written not too long ago by Sun Microsystem's Bill Joy in Wired Magazine, which dealt with genetic engineering, robotics and nanotechnology, and their ethical implications.

Dyson's new list of important things for us to 'worry' about gave way to the book's title. He looks "for ways in which technology may contribute to social justice..." by mitigating evils such as rural poverty. This chapter is a brilliant exercise in which Dyson puts his mind to fly and actually makes his vision very easy to grasp by non-technical readers. When you read through the chapter you can almost feel that his vision is happening already, although there are some very real and respectable hurdles still separating us from it, which need to be overcome.

CHAPTER 3: THE HIGH ROAD
Although the book consists of three chapters, the reason for the title is more aptly dealt with in chapters 1 and 2. Chapter 3 is a little out of context with respect to the original intention of the book, yet doesn't make the reader loose interest.

In this chapter, Dyson makes an incredible analysis and extrapolation about the elements surrounding our ability to find life beyond the boundaries of our planet. He believes, on the other hand, that as much as one hundred years would have to pass before we're near being able to send a significant amount of human explorers to space. But he doesn't leave readers without hope for this 'distant' future, as he lets his mind fly once again: He explains some of the exciting possible technologies he sees making massive human space exploration happen.

Finally, he wraps up chapter 3 with an ethical dissertation on the topics of cloning and reprogenetics (substituting chunks of live DNA with new, supposedly 'more desirable' chunks), closing it with the following brilliant yet slightly frightening words:
"To give us room to explore the varieties of mind and body into which our genome can evolve, one planet is not enough."

After such as closing sentence in chapter 3, I have to admit that the epilogue seemed a little weak, going back to topics already well discussed in chapter 2.

It is very easy throughout the entire book (which happens to take very little time to read, by the way) to be humbled by the ease with which Dyson deals with new scientific topics (for being a theoretical physicist, he jumps very easily, for example, from genetic engineering to space science) and the clarity he has (where some scientifics lack) in terms of the importance of maintaining the feet on the ground in the light of new scientific discoveries: how expensive will a new technology coming out of a discovery will be like, how many people will use it, etc.

After the death of Richard Feynman (some of whose books are among the 'scientific' books I've enjoyed the most) I thought the world had been deprived of its most brilliant teacher of science. Now I know Dyson is still with us, and this one only promises to become the first of his books I will read.

Dyson's books have always fascinated me by his wide-ranging intelligence, great insight, keen analysis and convincing arguments based on concrete examples. "The Sun, the Genome, the Internet" is not an exception. An additional agreeable character of his writing consists in the fact that he attaches importance to social justice realizable by technology. He expects that the gap between the rich and the poor would be narrowed by the ethical application of science.

In the final chapters of the book, Dyson discusses the future of the society under the inexorable growth of techniques suggested by the two big surprises that happened in 1997. These surprises are the cloning of Dolly and the defeat of the world chess champion by the IBM chess-playing program Deep Blue. The first of the surprises makes Dyson think about "reprogenetics," which is a possible future technology offering the parent the opportunity to improve the quality of life of the child by removing bad genes and by inserting advantageous ones. We cannot read Dyson's discussion about this possibility without reminding ourselves of the science fiction "Brave New World" by Aldous Huxley.

_The Sun, the Genome, and the Internet_ covers scientific
revolutions, technology & social justice, and the exploration &
colonization of space: familiar Dyson topics all, and delivered with
his usual grace. The three items in the title are Dyson's hope for
generating wealth in the world's poor villages: the sun for cheap
solar power, the Net to end rural isolation, and genetic engineering
for better crop plants. For example, he presents the hope of
engineering "trees that convert sunlight to liquid fuel and deliver
the fuel directly ...to underground pipelines." A neat solution to
declining oil reserves, if it works. Dyson cheerfully admits his
record as a prophet is mixed, but "it is better to be wrong than to be
vague."

Fresh and unexpected insights are a frequent pleasure in this
(and other) Dyson books. For instance, he describes his
mother and aunts, prosperous British matrons all, who, in the
interval between the World Wars, accomplished such things as
opening a birth-control clinic, managing a large hospital, winning
an Olympic medal, and pioneering aviation in Africa -- "it was
considered normal at the time for middle-class women to do
something spectacular." They were able to do this only with the
support of a large servant class. The introduction of labor-saving
appliances helped to emancipate the servants, but left middle-class
women less free than before, a general pattern, says Dyson: "the
burdens of equalization fall disproportionately on women."

Dyson is a lifelong space enthusiast, though things haven't gone
that well lately for space fans: "we look at the bewildered
cosmonauts struggling to survive in the Mir space station.
Obviously they are not going anywhere except, if they are lucky,
down." But in the long term, prospects are brighter, and await
finding a cheap way up and out of the gravity well (another
enduring Dyson insight). He reports recent successful tests of
a laser-launcher and a "ram accelerator", the latter a proposed 750-
foot gas-gun -- and a direct descendent of Jules Verne's cannon-
launched spacecraft in "From the Earth to the Moon"(1865). As in
all cheap launch methods, the trick is to keep the fuel on the
ground, not in the spacecraft. With cheap spacefight, people will
spread out into the solar system and beyond. Why? "Because it is
there" -- some folks just have itchy feet. Others will belong to
unpopular religions, or be on the run, or... any of the countless
other things that have always motivated emigrants.

Dyson, unusually for a theoretician, has always been more "tinker
than thinker". He cites Thomas Kuhn's classic _Structure of
Scientific Revolutions_ (1962, rev. ed. 1970) as an example of a

fellow-physicist with the opposite bent, emphasizing ideas over
things. Of course, both are important; but some of Kuhn's followers
put forward the idea that science is about power struggles, not new
ideas. Dyson once upbraided Kuhn about this at a conference. Kuhn
reacted angrily: "One thing you have to understand. I am not a
Kuhnian!"

Freeman Dyson is my favorite scientist-writer. I know of no one
else who combines his clarity of thought, graceful use of language,
big ideas expressed modestly, and sense of history. If you haven't yet
read Dyson, _The Sun, the Genome, and the Internet_ would be a
fine place to start. Highly recommended.
He is an emeritus professor
at the Institute for Advanced Study, Princeton University
and the author of many other books.
I would particularly recommend _Disturbing the Universe_ (1979)
and _Infinite in All Directions_ (1989), both among the very best
books ever written about science and its place in history, public
policy, and the exploration of space...