NOTE: I understand the role of random experiments in orthodox probability theory, and its role in providing unbiased estimators and hypothesis tests. Please don't answer this question with basic explanations of statistical testing.

Jaynes criticizes the role that random experiments are given by "orthodox" statisticians. He explains that randomization is in effect throwing away information, by making it prohibitively complex to reason about that information (e.g. by shaking around an urn of red and blue marbles, this makes it prohibitively complex to infer whether the next marble will be red or blue, since we would have to reason about the chaotic physical movements of those marbles in order to do so), and therefore can only lead to a less efficient estimate of parameters as compared to the correct Bayesian estimate that correctly reasons from the un-randomized data.

In other words, if we have unrandomized data concerning a certain parameter, randomizing it will only diminish one's knowledge of the parameter.

However, I cannot imagine that Jaynes actually rejects randomization, and he suggests that he doesn't on for example page 220 (end of section 7.13): "The real function of random experiment is to guard against completely unexpected bad effects about which our prior information gave us no warning"

However, I can't really find out what he considers the legitimate purpose of randomization is (within his Bayesian probability theory as extended logic).

So what is the purpose of randomization in Jaynes' view of Bayesian probability theory? How does he reconcile the need to randomize with his point that randomization merely "throws away information"?

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    $\begingroup$ Could you provide a direct quote and reference for Jaynes? $\endgroup$ – Tim Aug 6 '17 at 9:59
  • $\begingroup$ @Tim, a quote of him stating that randomization is throwing away information and decreases inference power? $\endgroup$ – user56834 Aug 6 '17 at 10:54

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