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On the Wikipedia page for conjugate prior there is a section "Analogy with Eigenfunctions", which describes a metaphor where observation of data is seen as a "linear operator" on the space of probability distributions, with conjugate priors as an eigenvector. Unfortunately, this section has no inline citations.

Does anyone know of any good references on the subject?

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    $\begingroup$ I have never seen this link made before and it does not seem to me to be mathematically justified. $\endgroup$ – Xi'an Dec 16 '18 at 20:04
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    $\begingroup$ The Wikipedia page makes it clear that the analogy is not a mathematical one: it has a somewhat fanciful, meta-mathematical nature. One wouldn't expect there to be references. $\endgroup$ – whuber Dec 16 '18 at 21:07

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