Darwinian John
You raise questions about Bibby and about Fisher.
Re Bibby: I have no view of the merits of Bibbifying Fisher's information but I am not surprised it got no attention. Mardia, Kent and Bibby's "Multivariate Analysis" was widely read but, speaking for myself and struggling to remember, I don't think I paid any attention to what I regarded as its conventional inference material. Sloppy reading, you might say, and open to Rao's criticism of Lindley as quoted in RAO-BLACKWELL THEOREM and RAO-BLACKWELLIZATION in http://jeff560.tripod.com/r.html.
Re Fisher: for him the primary form of information involved the second derivative rather than the square of the first derivative and so I can't see a natural analogue in his reasoning to your mutation.
John
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