When reporting a credibility interval, maybe also you, like I, are sometimes undecided between a 95%, a 90%, and an 89% interval (the last is common in the Bayesian literature). Well it turns out that the 89% interval has the following special property – for what it's worth:
Knowing whether the true value is within or without the 89% interval, corresponds to almost exactly 0.5 shannons of uncertainty (more precisely 0.4999 Sh). That is, the uncertainty is half that of a 50% credibility interval, measured on the log-scale of Shannon information.
The 90% interval corresponds to 0.469 Sh. The 95% one, to 0.286 Sh.
So if one reports 50% and 89% credibility intervals, one is reporting 1 Sh and 0.5 Sh of uncertainty.
The remarks above don't pretend to be more than a curiosity :)
[#]probability #bayes #informationtheory #rstats
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