Abstract
Recently, the conditional maximum-entropy method (abbreviated as C-MaxEnt) has been proposed for selecting priors in Bayesian statistics in a very simple way. Here, it is examined for extreme-value statistics. For the Weibull type as an explicit example, it is shown how C-MaxEnt can give rise to a prior satisfying Jeffreys’ rule.
Highlights
Understanding catastrophic events is a major goal of science of complex systems/phenomena
From the viewpoint of physics, the efforts made by Jeffreys [3] and Jaynes [4] are obviously of particular interest since they base their selection rule upon the invariance principle in “information geometry”, which somewhat reminds one of the measure of integration over spacetime in general relativity
In a recent paper [5], we have formulated a new method of selecting a prior, which is referred to as the conditional maximum-entropy method and is abbreviated as C-MaxEnt
Summary
Understanding catastrophic events is a major goal of science of complex systems/phenomena. A distribution is not invariant but accompanied by the Jacobian factor associated with a transformation of variables. In a recent paper [5], we have formulated a new method of selecting a prior, which is referred to as the conditional maximum-entropy method and is abbreviated as C-MaxEnt. This method has originally been motivated by nonequilibrium statistical mechanics of complex systems governed by hierarchical dynamics with largely-separated time scales [6,7,8].
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