Just a little note on ‘Tropical Bayesian Inference’.
Tropical Bayes and likelihood
Recently I wrote a short article on the foundations of profile likelihood because I was unsatisfied with the usual descriptions of it as ‘not a real likelihood’. Well, what is it? Why is it so useful (to some)? How should we interpret it? Etc.
It turns out that you can (arguably) think of likelihood in terms of possibility theory, rather than probability theory, and that possibility theory is naturally formulated in terms of the (somewhat obscure) mathematical languages of maxitive measure theory, idempotent probability theory and tropical algebra/tropical geometry.
Once you replace probability by possibility, everything works out basically exactly the same as in standard Bayesian inference. Hence in a recent revision I decided to call it ‘Tropical Bayes’.
You can read the preprint here.