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Cox begins the book by discussing his axioms, and then expressing them as functional equations. The solution of these functional equations develops the theory to the point at which Laplace began his own development.
(In general, the probability of a proposition is conditional on the truth of some other proposition. An item of particular interest here is that while most Bayesian expositions call this a priori true proposition "prior information", Cox calls this proposition the "hypothesis". This term seems to me to be more sensible, because we are rarely absolutely certain about our prior information. We take our "prior information" to be true, not because we are certain it is true, but as a conjectural point of departure for the subsequent calculation.)
Cox continues the development of the theory by relating the notion of probability to information entropy. He gives a definition for systems of propositions and shows how entropy is related to the uncertainty as to which of the propositions in the defining set of the system is true. (By hypothesis, at least one proposition in the defining set is true.)
Cox finishes the book with a section on expectation. He shows here how the theory he has developed encompasses all of the standard results of expectations found in other theories of probability.
This book looks deceptively thin, but packs the punch of a ten-pound textbook. It requires multiple passes (or, perhaps, one pass, closely read) in order to get all of the information out of it. It is definitely an exposition of an algebra, that is to say, an abstract symbolic method of calculation. Sometimes Cox gives concrete examples to illustrate the abstract reasoning, and sometimes he doesn't. Where he doesn't, the reader is left to puzzle out the concrete consequences of the abstract reasoning. I'm not sure if this is good or bad, but I'm leaning towards good, even though it does make my brain hurt.
explains why I have my present position at MIT. But I
cannot write book reviews the way Rota did.
Why should the conventional sum and product rules of
probability hold when probabilities are assigned, not
to *events* that are *random* according to their
relative frequencies of occurrence, nor to subsets of
populations as proportions of the whole, but rather
to *propositions* that are *uncertain* according to the
degree to which the evidence supports them? The tenet
that the same rules should apply to such "degrees of
belief," whether they are "subjective" probabilities or
"logical" probabilities, is the essence of Bayesianism.
The relative merits of Bayesian and frequentist methods of
statistical inference have been debated for decades. But
seldom is the question with which I started this paragraph
addressed. Several answers to that question have been
proposed. Richard Cox's book embodies one of them.
Many writers on foundations of statistical inference are
callously imprecise about the kind of topic dealt with
in this book. Cox is their antipode, writing not only
clearly, but supremely efficiently, beautifully, perhaps
sometimes poetically, about functional differential
equations and about delicate philosophical questions.
Cox also deals with the relationship between entropy and
distributive lattices. Shannon entropy is to distributive
lattices as probability is to Boolean algebras. I do not
think Cox was familiar with standard work on lattice theory.
He never uses the word "lattice," nor other standard
lattice-theory nomenclature.
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Richard Cox brings years of professional archival practice and scholarship to bear on the fallacies of "Double Fold". Cox rationalizes the debate by asking profound questions about how society should decide what it preserves among competing wants with limited resources, the best methods for preservation, and what the implications for Baker's solution of "saving everything" will be in our electronic age.
Most interesting perhaps is Cox's review of Nicholson Baker's public statements on the TV and lecture circuit regarding his "Double Fold" crusade. Obviously, consistency is not one of Baker's hobgoblins. He seems to have made a career out of repeatedly contradicting what he wrote in "Double Fold". Of extreme value in Cox's response is his focus on how Baker has brought the previously private library science debate on what materials to preserve and how into the public realm. Although he disagrees with Baker's caricature of librarians, Cox argues that the public perceptions of librarianship and archival responsibilities should be of extreme concern to the profession.
Cox doesn't just do a hatchet job. He uses "Double Fold" with all its warts as part of his graduate courses for archivists. Cox believes that Baker has done the profession a favor by shaking it up a bit and bringing preservation issues into public debate. The only criticism I have of the book is that its arguments are at time redundant.
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I would advise people using this and other Wrox "Beginning" books to have other reference books on hand, when concepts spring up without sufficient explanation. Also, spend more time with the examples and try to use the examples to write your own unique programs before moving on. It will take a little longer, but you'll learn better and faster in the long run.
Anyone who finishes this book to be able to write pretty much anything they please. It shows you stuff from small utilities for the command line to full GUI-driven database apps. There is a section on writing device drivers and kernel hacking, there's also another section on writing HTML. It really is that broad and encompassing, I refer to it time and time again.
Although this book is called 'Beginning Linux Programming', it's clear that a lot of the skills you'll gain from this book are transferable to other platforms, thanks to POSIX, X/Open, et al.
One possible criticism is that KDE programming is not covered (except, the TCL/TK programs will obviously work under KDE, as will the GNOME programs if you have the correct libraries installed). However, the book had to end somewhere, and for the bang-per-buck (this is a big book) the value-for-money is quite amazing.
And, to top it all off, it has a foreword by Alan Cox, Linux demi-god uber-geek. If that's not a recommendation, nothing is!
One caveat - it says it's for beginners, but almost all of the examples are in C, using some pretty advanced constructs. If you're still rusty with pointer syntax (for example), brush up on your C programming first. Also, like most Linux source, the examples are in straight-C rather than C++, but this is probably a Good Thing.
Also, there's a chapter at the end on writing device drivers - I couldn't get any of the examples to compile on my Redhat system running kernel version 2.4.9; I guess they're due for another edition of this book.
All in all, one of the best computer books I've ever read!
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"John Locke has been called America's philosopher, our king in the only way a philosopher has ever been king of a great nation." - Robert A Goldwin
The intent of this review is not to familiarize you with the political philosophy of John Locke, for such a task would require far more than 1,000 words and has already been done elsewhere by others far more qualified than I. This review is for those who have already decided to purchase the Second Treatise but are unaware of the difference between the Peardon (Library of Liberal Arts), Cox (Crofts Classics), and MacPherson (Hackett) editions of the text.
The Cox and MacPherson editions are strikingly similar; however, Cox has taken the liberty of modernizing the text and in the process seems to have misplaced a few words. Peardon, on the other hand, seems to have modernized so much as to have completely lost most of Locke's italicization. So, it is my recommendation to purchase the MacPherson edition. That, or go read the hand-corrected copy of the third printing which is kept in the library of Christ's College, Cambridge University. Unfortunately, the pages in the MacPherson edition are a tad thin, and highlighters seem to leak through the pages. So, if you tend to make good use of highlighers, then you should probably purchase the Cox edition because the library at Christ's College definitely will not allow you to write on their copy.
"John Locke has been called America's philosopher, our king in the only way a philosopher has ever been king of a great nation." - Robert A Goldwin
The intent of this review is not to familiarize you with the political philosophy of John Locke, for such a task would require far more than 1,000 words and has already been done elsewhere by others far more qualified than I. This review is for those who have already decided to purchase the Second Treatise but are unaware of the difference between the Peardon (Library of Liberal Arts), Cox (Crofts Classics), and MacPherson (Hackett) editions of the text.
The Cox and MacPherson editions are strikingly similar; however, Cox has taken the liberty of modernizing the text and in the process seems to have misplaced a few words. Peardon, on the other hand, seems to have modernized so much as to have completely lost most of Locke's italicization. So, it is my recommendation to purchase the MacPherson edition. That, or go read the hand-corrected copy of the third printing which is kept in the library of Christ's College, Cambridge University. Unfortunately, the pages in the MacPherson edition are a tad thin, and highlighters seem to leak through the pages. So, if you tend to make good use of highlighers, then you should probably purchase the Cox edition because the library at Christ's College definitely will not allow you to write on their copy.
Any student of American history, particularly of the revolution and the formation of the Constitution, out of necessity should read this book. It is a book that the revolutionaries themselves were well acquainted with, and formed the rational basis for justifying both the Revolution and the establishment of the Constitution.
Locke is, also, suprisingly easy to read, even today. Cogent, well-formed arguments inform every page of this masterwork. This is a fascinating book that shaped history itself.
What Cox accomplishes in this deceptively slim volume is amazing. He places Bayesian probability theory on an axiomatic foundation, as a natural extension of Boolean logic, identifying probabilities with degrees of subjective belief in propositions rather than directly with frequencies of events (though he also argues that the subjectivist interpretation accords with the frequentist interpretation whenever the latter makes sense at all).
Essentially, he shows that the ordinary laws of probability theory are normative laws of thought that apply to degrees of belief in propositions, and that we have to conform to them if we want to think consistently.
If you like math and logic books, you'll find this one eminently readable; I haven't seen it in years and yet I still remember the stunning clarity of Cox's rigorous exposition.
This is the book that originally sold me on Bayesianism. If you have any interest in this subject at all, grab this one while it's available.