Theory of Probability

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1. kqrAug 2024
   I second both The Signal and the Noise as well as How to Measure Anything. I also mentioned upthread Willful Ignorance.

   I think perhaps the best bang for your buck could be Wheeler's Understanding Variation -- but that is based mainly on vague memory and skimming the table of contents. I plan on writing a proper review of that book in the coming year to make certain it is what I remember it to be.

   I think the earlier works by Taleb also touch on this (Fooled by Randomness seems to have it in the title).

   But then I strongly recommend branching out to places where these fundamentals are used, to cement them:

   - Anything popular by Deming (e.g. The New Economics)

   - Anything less popular by Deming (e.g. Some Theory of Sampling)

   - Moneyball

   - Theory of Probability (de Finetti)

   - Causality (Pearl)

   - Applied Survival Analysis

   - Analysis of Extremal Events

   - Regression Modeling with Actuarial and Financial Applications

   The more theoretical and applied books are less casual reads, obviously. They also happen to be the directions in which I have gone -- you may have more luck picking your own direction for where to apply and practice your intuition.

   Edit: Oh and while I don't have a specific book recommendation because none of the ones I read I have good opinions on, something on combinatorics helps with getting a grasp on the general smell of entropy and simpler problems like Monty Hall.

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2. kqrAug 2023
   Read lots of books. Reading just one book you'll walk away with gaps in your understanding you don't even know are there. A mentor can point them out for you and give you directions on how to close them, but absent that you have to approach everything from as many angles as you can and hope that you will fill in the gaps by sheer luck. (That's a coupon collector's problem for you!)

   I recently re-read and took extensive notes on de Finetti's Theory of Probability which I always recommend. But don't stick to just that.

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3. kqrOct 2022
   This was much more common in the first 2/3 of the 20th century than it is today. I can strongly recommend Theory of Probability (de Finetti, compiled 1970 based on work de Finetti did as early as 1930s) and Foundations of Statistics (Savage, 1972) – the latter leans a bit on the former but expands on it with useful perspectives.

   I recommend you start with these basic theoretical books to get a sense of what it's all built on. But then if you want more practical advice about how to handle things, books on sampling theory tend to hit a sweetspot between theory and practise, in my experience. I like Sampling Techniques (Cochran, 1953) and Sampling of Populations (Levy & Lemeshow, 2013).

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4. kqrMay 2021
   I've been brought up in a strictly classical/frequentist/objectivist school of inference and testing. The last few months, I've begun expanding my perspectives into subjective probability, decision analysis, Bayesian methods, causality analysis, and some information theory.

   These things have helped me understand probability and statistics a lot better. Some examples of books that have been useful include,

   - Understanding Uncertainty (Lindley 2009),

   - Theory of Probability (de Finetti 1975),

   - Foundations of Statistics (Savage 1953),

   - Computer Age Statistical Inference (Efron),

   - Causality (Pearl 2011),

   - Trustworthy Online Controlled Experiments (Kohavi et al.)

   However, most of this is about one "person" dealing with "the world", which in turn is neutral. I want to learn more about the situation where two "people" are in an antagonistic/competitive relationship.

   I mention these to give an idea of what sort of book I'd prefer: I want to go into technical detail, but I don't need everything to be proved from axioms. I will eventually use the tools I learn in practise, but I do want an intuitive sense of what they mean and how they are constructed, and I'm prepared to work a little bit for it.

   If I can't get a better suggestion here, von Neumann's classic on the subject is where I'll go.

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5. kgwgkJun 2019
   For the hard way, look at Bruno de Finetti's Theory of Probability:

   https://onlinelibrary.wiley.com/doi/book/10.1002/97811192863...

   Jaynes is certainly very deep and some sections are harder than others. It's interesting regardless of your level (this is a book worth rereading several times).

   For a less technical, but full of insight, introduction see Dennis Lindley's Understanding Uncertainty:

   https://onlinelibrary.wiley.com/doi/book/10.1002/97811186501...

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6. stakhanovJul 2018
   "Theory of Probability" by Bruno de Finetti is the best text on probability ever written.
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