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Probability Theory: The Logic of Science

4.39  ·  Rating details ·  564 ratings  ·  19 reviews
Going beyond the conventional mathematics of probability theory, this study views the subject in a wider context. It discusses new results, along with applications of probability theory to a variety of problems. The book contains many exercises and is suitable for use as a textbook on graduate-level courses involving data analysis. Aimed at readers already familiar with ap ...more
Hardcover, 753 pages
Published April 10th 2003 by Cambridge University Press (first published April 9th 1999)
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Justin The equations before 2.16 involve differentiation and continuity, which are introduced early on in the calculus sequence, and rigorously defined in th…moreThe equations before 2.16 involve differentiation and continuity, which are introduced early on in the calculus sequence, and rigorously defined in the study of analysis.

The book is targeted towards scientists, grad students, or "advanced undergraduates," so I think it would be difficult to attempt it without previous university-level math exposure.

I'm taking 3rd year math courses at my University, but this book may be above where I'm at as well. I'll probably read it at some point, when I finish my next stats class that has an emphasis on probability. If I can make sense of the equations I'll let you know.(less)

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Paul
Mar 30, 2013 rated it it was amazing
Folks who follow me on Twitter know this is essentially my 2nd bible. (Yes, the first one is The Bible.)

There's really no way to delve into that other than to recapitulate the book, but let me just hammer one point, which I take to be central, home: good old-fashioned Aristotelian two-valued logic is a special case of probability theory properly understood. Conversely, probability theory properly understood is a generalization of good old-fashioned Aristotelian two-valued logic.

Jaynes makes no c
...more
Joshua
May 13, 2016 rated it it was amazing
A "frequentist," according Jaynes, is someone who believes in random variables. That would be just about anyone who uses probability theory, right? "No," Jaynes would say. It's anyone who uses orthodox probability theory. The alternative, espoused here, is to consider probability as a measurement for propositions about reality. I'm afraid that I'm not going to be able to explain it any better than that, but if you read the first two chapters of this book, you will concede that it's a neat idea. ...more
Dana Larose
May 06, 2010 marked it as to-read
*sigh* Why do I love adding math books I'm most likely not smart enough to understand? ...more
Jake
Dec 28, 2015 rated it it was amazing
“Our theme is simply: probability theory as extended logic. The ‘new’ perception amounts to the recognition that the mathematical rules of probability theory are not merely rules for calculating frequencies of ‘random variables’; they are also the unique consistent rules for conducting inference (i.e. plausible reasoning) of any kind, and we shall apply them in full generality to that end.” - E.T. Jaynes’

As an undergraduate in computer science, I left my statistics course with disdain. The curri
...more
Benson Lee
May 19, 2015 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.. why would I be reading a book about Bayesian statistics if I thought it was a waste of time, and why do I need to read about application of these ideas to determining whether ESP is real or not? Anyway, st ...more
yash kalani
Oct 29, 2018 rated it it was amazing
This book took my brain apart and rebuilt it.
Eric
Jul 19, 2017 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. ...more
Dani Mexuto
Nov 24, 2016 rated it it was ok
Entendo mellor os Youtubes
Marius
Mar 07, 2019 rated it it was amazing
What do I need to know to be able to read this book?
Hamish Seamus
May 04, 2021 is currently reading it
Further reading:
My interest in probability theory was stimulated first by reading the work of Harold Jeffreys (1939) 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. T. Cox (1946), Shannon (1948) and Po ́lya (1954) opened up new worlds of thought, whose explo- ration has occupied my mind for some 40 years.


In summary, qualitative correspondence with common sense requires that
...more
Matthew Geleta
Nov 20, 2020 rated it it was amazing
For all its flaws, this is and absolutely outstanding as a piece of mathematical exposition. Admittedly it's a little verbose in places, and the author sometimes comes across as arrogant in his critique of other academics - those who adhere to frequentist rather than Bayesian interpretations of probability, or those who fall into the trap of mind projection fallacy, to cite two examples. However, the quality of exposition more than makes up for this stylistic choice. I gained a far deeper unders ...more
Will Dorrell
May 19, 2020 rated it really liked it
Textbook by a staunch Bayesian describing his approach to probability/statistics from the ground up.

He's a feisty one, and spends a fair bit of his time attacking various viewpoints. It's quite fun to read the first few times, but he definitely repeats himself.

The content is nice though, I feel I finally understand what those messy things like p-values, chi squared tests etc are.
...more
Zach
Apr 19, 2021 rated it it was ok
The math is a bit above my head, but I still got a few things out of this. I have a much better grasp of the Bayesian vs Frequentist approach. I really like Jaynes' approach of decoupling information from physical reality, which is neither subjective or objective. It's prior knowledge all the way down. But I don't have a dog in any of these fights. ...more
Doug
Jun 18, 2009 rated it it was amazing
Shelves: text-books
This is a must read for anyone claiming to be a probabilist.
Foppe
Sep 20, 2010 marked it as home-library
Review can be found here. ...more
Francisco Tapiador
Nov 13, 2011 rated it it was amazing
This book is going to be huge in the next twenty years. Just keep tuned.
Steve Davidson
Dec 05, 2016 rated it it was amazing
Best book on statistics ever.
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Edwin Thompson Jaynes was the Wayman Crow Distinguished Professor of Physics at Washington University in St. Louis. He wrote extensively on statistical mechanics and on foundations of probability and statistical inference, initiating in 1957 the MaxEnt interpretation of thermodynamics, as being a particular application of more general Bayesian/information theory techniques (although he argued this ...more

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