Statistical model validation is treated for a general class of nonparamet-ric uncertainty models. This problem is shown to reduce, in many cases of interest, to computing the limit of a sequence (V k) 1 1 of relative weighted volumes of convex sets in R k. An associated decision problem is shown to reduce to a pair of likelihood ratio tests. The notion of testability is introduced to describe u...

This lecture is about some of the basics of uncertainty: the use of variances and covariances to express statistical uncertainty (“error bars”, error ellipses); we are concentrating on the uncertainties of geographic co-ordinates. This makes it necessary to talk about geodetic datums – alternative ways of fixing the starting point(s) used for fixing geodetic co-ordinates in a network solution. ...

Abstract Uncertainty can be classified as either aleatoric (intrinsic randomness) or epistemic (imperfect knowledge of parameters). The majority frameworks assessing infectious disease risk consider only uncertainty. We ever observe a single epidemic, and therefore cannot empirically determine Here, we characterise both uncertainty using time-varying general branching process. Our framework exp...

This Chapter presents the PASCAL Evaluating Predictive Uncertainty Challenge, introduces the contributed Chapters by the participants who obtained outstanding results, and provides a discussion with some lessons to be learnt. The Challenge was set up to evaluate the ability of Machine Learning algorithms to provide good “probabilistic predictions”, rather than just the usual “point predictions”...