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I am currently learning about Bayesian methods. One of the first clear distinctions is the lack of hypothesis testing and usage of sampling distributions.

I began to wonder about the approach to designing experiments from the Bayesian point of view. In my experimental coursework we discuss power and sample size selection but without hypothesis testing how do we assess sample size.

Does anyone know of educational resources on the topic of Bayesian Experimental Design? I found the following papers and curious if there is good textbook on the topic to offer a fundamental introduction.

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    $\begingroup$ There's a great (albeit somewhat dated) textbook on Bayesian Approaches to Clinical Trials by Spiegelhalter et al. $\endgroup$
    – Durden
    Commented Sep 27, 2023 at 20:19
  • $\begingroup$ @ Durben thanks for sharing this textbook it offers some good information $\endgroup$
    – Vefeagins
    Commented Sep 28, 2023 at 5:16
  • $\begingroup$ Many experiments in physics, chemistry and other sciences actually do not involve hypothesis testing - at least not explicitly. E.g., if a mathematical theory predicts a peak in a certain place under certain conditions, and an experimentalist observes it. This could be considered as an overwhelming evidence in favor of the hypothesis, but could be equally well interpreted in terms of Bayes factors, posterior, etc. It is pushed even further when physicists speak of self-averaging, where a single sample can actually be treated as an ensemble - due to its size or averaging by fluctuations. $\endgroup$
    – Roger V.
    Commented Sep 28, 2023 at 7:47

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It's not a textbook wholly on this topic, but Chapters 11.4 - 11.5 of Jay Kadane's Principles of Uncertainty are meant to introduce a Bayesian perspective on experimental design (how should you choose a sample size if you want to convince another Bayesian who has a different prior than you do?) and randomization (in what sense might a Bayesian care about whether units were randomized to treatments?):

https://www.stat.cmu.edu/~kadane/principles.pdf

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    $\begingroup$ Thanks for sharing I liked the Bayesian Approaches to Clinical Trials book as well $\endgroup$
    – Vefeagins
    Commented Oct 3, 2023 at 19:14

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