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Exploring the work of ET Jaynes, Probability Theory (11th Printing 2013) has led to consideration of the technique he identifies as Sequential Inference (p. 96); where the evidence, in decibels, accumulates until the investigator either (1) stops with acceptance, (2) stops with rejection or (3) continues with another test. Jaynes' technique appears to be a special case of, and perhaps a more Bayesian approach than, sequential analysis as proposed by Abraham Wald. But I am certainly not an expert here.

This looks to be an incredibly powerful technique that can be used to investigate a claim of compliance/non-compliance in a cost effective and time efficient manner. Yet when searching the internet and also checking other Bayesian texts (such as Silvia and Skilling) there is little depth on it, if it is mentioned at all.

So these questions are posed:

(1) Is it used in practice?

(2) If so, in what way, if not, why not?

(3) Are there critical issues/pitfalls with it's use in practice?

(4) Is (are) there any in-depth reference(s) with case studies of application?

Addendum

Since posting this earlier, we have found an excellent collection of information here.

Coming from an engineering background, by nature we tend to be data driven, and this would put Engineers solidly in the Frequentist camp. However, time and again we have seen that these analyses should start from a position of logic, and this is what a proper Bayesian approach will accomplish, it is clear. So there is no doubt in our mind that the Bayesian method trumps the Frequentist one.

However, what we are specifically interested in is the concept of evidence in decibels (it seems that bels or maybe the Jaynes Scale (0,10] analogous to the Richter Scale might have been a more interesting way to consider it).

But is this approach used for more routine issues found in practice, and are there any case studies of such?

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    $\begingroup$ I'm still learning about this, but from what I read this technique was used by Turing in cracking the Enigma code. Turing's method was classified due to the war, but was also discovered by Wald (1947, sequential analysis). Recent research by Michael Shadlen suggests that neurons or clusters of neurons use this method. I couldn't find that page number in E.T. Jaynes's Probability Theory (different edition). Could you share which chapter/section discusses sequential inference or sequential analysis? $\endgroup$ – Julien Couvreur Mar 29 '14 at 19:35
  • $\begingroup$ @Julien Couvreur - From 'Probability Theory', ET Jaynes, 11th Printing, 2013 - Chapter 4, P. 86 - 'sequential inference' is first mentioned within the last paragraph of p. 96. Evidence is quantified in Table 4.1, p. 93. $\endgroup$ – AsymLabs Apr 25 '14 at 19:59
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Yes, it's used. See e.g., discussion and examples in Wagenmakers et al, pdf available at OSF.

I'm aware that this is a link-only answer, but hope it is nevertheless of value.

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