  The extrapolation of extremes to values beyond the span of stationary
univariate historical data is considered from Bayesian and Frequentist
perspectives. The intention is to make predictions which in some sense
"preserve probability". A Frequentist approach based on a simple curve-fit
estimate of the tail parameter $\xi$ of a Generalised Pareto Distribution was
described in McRobie (2014) (arXiv:1408.1532). In this paper, the corresponding
Bayes-like approach is described, using a plausible noninformative prior for
the tail parameter. The two approaches, though philosophically different, show
a reasonable degree of correspondence.
