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I am from physics background. I know basics about statistics (upto 'Statistical Inference - Casella'). I came across some articles talking about terms like 'reciever operating characteristics curve', 'True-positive, True-negative, False-positive, and False-negative'. I want to understand those concepts from basics to do some calculations for the present project that I am working. I have read the section on 'Decision Theory' from Introduction chapter of Bishop's book 'Pattern Recognition and Machine Learning'. I need a little detailed reading. Not so theoretical and small in volume. Which book will be great?

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  • $\begingroup$ I’ll make a suggestion of MathematicalMonk’s videos, though I’m not sure how the level compares with Casella. youtube.com/watch?v=KYRAO8f5rXA $\endgroup$
    – Dave
    Feb 8 '20 at 23:16
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Decision Theory: Principles and Approaches by Giovanni Parmigiani and Lurdes Inoue sounds like what you are looking for. For depth on the Bayesian side, I would recommend The Bayesian Choice by Robert.

Unfortunately, I do not do enough work on the Frequentist side to need a deeper book on the Frequentist side. There is an overwhelming argument for the use of Bayesian methods in my work, so even though I am trained primarily on the Frequentist side, I use it much less frequently and never in a decision-theoretic framework.

Hopefully, someone will post a deeper Frequentist work because while you are violating the likelihood principle (which is itself controversial) you are not required to make strong distributional assumptions in order to determine what behaviors you should engage in.

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Those two books provide nice introduction to decision theory, but with statistical focus, that emphasize Bayesian statistics:

James O. Berger.
Statistical Decision Theory.
Springer.

Christian P. Robert.
The Bayesian Choice.
Springer.

Those are nice introductory handbooks on decision theory in general, with less, or no reference to statistics:

Martin Peterson.
An Introduction to Decision Theory.
Cambridge University Press.

Herman Chernoff and Lincoln E. Moses.
Elementary Decision Theory.
Dover.

David A. Blackwell and M.A. Girshick.
Theory of Games and Statistical Decisions.
Dover.

The choice depends on how deep you want to go into the subject and if you are looking for a statistics oriented book, or not.

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