Probability theory the logic of science ebook download

Fisher and the frequentist school by reading the perspective of biologists and other statistical professionals who employ both Bayesian methods and Frequentest. Jaynes' view does not seem discredited but it is a much more complicated and nuanced issue than I first gave it credit for.

May 19, Benson Lee rated it really liked it. It's a good book - it approaches probability from the right direction and develops interesting, useful results. However, the author is often wordy and spends a bunch of time trying to convince the reader why the Bayesian interpretation of statistics is superior to frequentist interpretations.. Anyway, st It's a good book - it approaches probability from the right direction and develops interesting, useful results.

Anyway, still good book, just dinged for 1 sometimes wild tangents and 2 sometimes lengthy derivations whose final formulation does not reveal much interesting insight into the nature of the problem. Oct 29, yash rated it it was amazing.

This book took my brain apart and rebuilt it. Jul 19, Eric rated it it was amazing. Jaynes' tome on Bayesian Statistics and its underpinnings. A really important text for me while I was working on my PhD. I found a lot of really useful guidance here on assigning prior probabilities and using maximum entropy principles.

It's also just fun to read. Jaynes has a strong voice and is a bold shit-talker when it comes to the short-comings of traditional frequentist statistics. Mar 07, Marius rated it it was amazing. What do I need to know to be able to read this book? View 2 comments. Nov 24, Dani Mexuto rated it it was ok.

Entendo mellor os Youtubes. May 04, Hamish rated it really liked it Shelves: non-fiction , read-manually , maths , textbook , worth-re-reading. What a book! The most difficult book I've ever read, ahead of Reasons and Persons by a decent margin.

But fascinating and thought provoking. After about chapter 2 I gave up on being able to follow the details of the proofs. Jaynes uses combinatorics, real analysis, measure theory, Laplace transformations, Fourier transformations, linear algebra, group theory, thermodynamics, and just about any branch of mathematics that suits his purposes. To understand everything I would need to spend at least a What a book! To understand everything I would need to spend at least a year laboriously going through each derivation on a blackboard.

To just absorb the commentary and "style" of the proofs has already taken me almost three months, minutes per day. I think I'd like to come back and re-read Jaynes after I've got more background in probability theory and statistics. But for now God it feels good to be finished with Jaynes. Further reading: My interest in probability theory was stimulated first by reading the work of Harold Jeffreys and realizing that his viewpoint makes all the problems of theoretical physics appear in a very different light.

But then, in quick succession, discovery of the work of R. In summary, qualitative correspondence with common sense requires that w x [ As the reader may check, we could just as well have chosen the opposite convention; and the entire development of the theory from this point on, including all its applications, would go through equally well, with equations of a less familiar form but exactly the same content. Aristotelian deductive logic is the limiting form of our rules for plausible reasoning, as the robot becomes more and more certain of its conclusions.

If you're computing the probability of drawing a red ball from an urn, then you use the hypergeometric distribution with the number of red and non-red drawns so far as parameters. If I'm understanding Jaynes correctly, then if you also knew whether the draw after your current draw was red or non-red, you would update your probability of the current draw in exactly the same way as if the future draw was a past draw.

Yet the urge to follow the vernacular and treat it as plural is sometimes irresistible, and so we shall be knowingly inconsistent and use it both ways, judging what seems euphonious in each case. Apropos of little: For an interesting account of the life and work of Gustav Theodor Fechner —87 , see Stigler c. Jaynes is There is a long history of workers who did seemingly obvious things in probability theory without bothering to derive them by strict application of the basic rules, obtained nonsensical results — and concluded that probability theory as logic was at fault.

The greatest, most respected mathematicians and logicians have fallen into this trap momentarily, and some philosophers spend their entire lives mired in it. As Gauss stressed long ago, any kind of singular mathematics acquires a meaning only as a limiting form of some kind of well-behaved mathematics, and it is ambiguous until we specify exactly what limiting process we propose to use.

Should "Bayesian statistics" really be called Laplacian statistics? Or maybe Bernoullian statistics? It appears that this result was first found by an amateur mathematician, the Rev.

Thomas Bayes We shall follow this long-established custom, although it is misleading in several respects. The general result 4. Furthermore, it was not Bayes but Laplace who first saw the result in generality and showed how to use it in real problems of inference.

Page has the derivation for a normal approximation of a beta distribution. Page has a useful Stirling approximation of the binomial distribution. The following page mentions that the chi-square test relies on the exponential approximation of the binomial, which itself is a MacLauren approximation around the mode.

Thus it is not accurate far from the mode, and can be abused to under-estimate the likelihood of the null hypothesis. Perhaps this is the fundamental difference between Bayesians and Frequentists? A practical difficulty of this was pointed out by Jeffreys ; there is not the slightest use in rejecting any hypothesis H0 unless we can do it in favor of some definite alternative H1 which better fits the facts.

The most familiar problems may be so complicated — just because the result depends on so many unknown and uncontrolled factors — that a full Bayesian analysis, although correct in principle, is out of the question in practice. In recent years there has grown up a considerable literature on Bayesian jurisprudence; for a review with many references, see Vignaux and Robertson Likewise, the first law of thermodynamics, in showing us the limits of validity of the caloric theory, also confirmed the accuracy of the caloric theory within its proper domain processes where heat flows but no work is done.

Laplace's rule of succession also applies when for predicting the next draw from an Urn. See p A common and useful custom is to use Greek letters to denote continuously variable parameters, Latin letters for discrete indices or data values Huh. I never noticed that. A reason to prefer absolute-error minimisation over square-error minimisation is that only the former is reparameterization invariant.

This is quite a nice statement of the difference between Bayesians and frequentists: "When I toss a coin, the probability for heads is one-half.

Over the past two centuries, millions of words have been written about this simple question. Then why should anyone ever want to buy insurance?

Original origin of VNM utility? This is not to say that the problem has not been discussed; de Groot notes the very weak abstract conditions transitivity of preferences, etc. Long ago, L. Savage considered construction of utility functions by introspection. This is described by Chernoff and Moses : suppose there are two possible rewards r1 and r2; then for what reward r3 would you be indifferent between r3 for sure or either r1 or r2 as decided by the flip of a coin?

Presumably, r3 is somewhere between r1 and r2. If one makes enough such intuitive judgments and manages to correct all intransitivities, a crude utility function emerges. Berger , Chap. If we wish to consider an improper prior, the only correct way of doing it is to approach it as a well-defined limit of a sequence of proper priors.

Whence the arguments between Jeffreys Bayesian and Fisher frequentist? Firstly, we need to recognize that a large part of their differences arose from the fact that Fisher and Jeffreys were occupied with very different problems. Jeffreys studied problems of geophysics, where one had a great deal of cogent prior information and a highly developed guiding theory all of Newtonian mechanics giving the theory of elasticity and seismic wave propagation, plus the principles of physical chemistry and thermodynamics , and the data taking procedure had no resemblance to drawing from an urn.

Fisher, in his cookbook , Sect. Was Fischer evil? In any field, the most reliable and instantly recognizable sign of a fanatic is a lack of any sense of humor. Colleagues have reported their experiences at meetings, where Fisher could fly into a trembling rage over some harmless remark that others would only smile at.

Jan 10, Christian Adriano rated it it was amazing Shelves: statistics. Page "There is another aspect in which loss functions are less firmly grounded than are prior probabilities. We consider it an important aspect of 'objectivity' in inference - almost a principle of morality - that we should not allow our opinions to be swayed by our desire; what we believe should be independent of what we want. But the But the converse need not be true; on introspection, we would probably agree that what we want depends very much on what we know, and we do not feel guilty of any inconsistency or irrationality on that account.

But after learning about the behavior of men, he wished instead that he had been made a whole gargoyle. In other words, after gaining knowledge, he changed his wants. However, his wants did not define his knowledge beliefs.

The foundations of statistics are in a state of profound conflict. Fisher's objections to some aspects of Neyman-Pearson statistics have long been well known. More recently the emergence of Bayesian statistics as a radical alternative to standard views has made the conflict especially acute. In recent years the response of many practising statisticians to the conflict has been an eclectic approach to statistical inference.

Many good statisticians have developed a kind of wisdom which enables them to know which problems are most appropriately handled by each of the methods available. The search for principles which would explain why each of the methods works where it does and fails where it does offers a fruitful approach to the controversy over foundations.

Twenty-nine collected essays represent a critical history of Shakespeare's play as text and as theater, beginning with Samuel Johnson in , and ending with a review of the Royal Shakespeare Company production in In this book Pollock deals with the subject of probabilistic reasoning, making general philosophical sense of objective probabilities and exploring their relationship to the problem of induction.

He argues that probability is fundamental not only to physical science, but to induction, epistemology, the philosophy of science and much of the reasoning relevant to artificial intelligence. Pollock's main claim is that the fundamental notion of probability is nomic--that is, it involves the notion of natural law, valid across possible worlds. The various epistemic and statistical conceptions of probability, he demonstrates, are derived from this nomic notion.

He goes on to provide a theory of statistical induction, an account of computational principles allowing some probabilities to be derived from others, an account of acceptance rules, and a theory of direct inference. Of course, this implies that, if one succeeds in demonstrating convincingly the pseudo-character of a problem by giving its 'solution', the time spent on it need not be seen as wasted. We conclude this section with a brief statement of the criteria for concept explication as they have been formulated in several places by Carnap, Hempel and Stegmiiller.

Hempel's account [13J, Chapter 1 is still very adequate for a detailed introduction. The process of explication starts with the identification of one or more vague and, perhaps, ambiguous concepts, the so-called explicanda. Next, one tries to disentangle the ambiguities.

This, however, need not be possible at once. Ultimately the explicanda are to be replaced not necessarily one by one by certain counterparts, the so-called explicata, which have to conform to four requirements. They have to be as precise as possible and as simple as possible. In addition, they have to be useful in the sense that they give rise to the formulation of theories and the solution of problems.

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