Given a dataset generated by various processes, an estimate of the quantity of data points associated with each generation process can be achieved using a probabilistic count of evidence using Bayes Theorem. However, the usefulness of these counts is limited by the presence of uncertainties stemming from the determination of quantities using maximum likelihood and the imprecision of density est...

pected disease is common or not, and whether the findings tend to support or discount this hypothesis. Such intuitive procedures may be, and often are, seriously biased1. It would be preferable to employ an open system where all the assumptions about diagnostic reasoning, and the way in which they are combined, are made quite explicit. Bayes theorem2 provides such a model. An understanding of h...

We propose a PAC-Bayes theorem for the sample-compression setting where each classifier is described by a compression subset of the training data and a message string of additional information. This setting, which is the appropriate one to describe many learning algorithms, strictly generalizes the usual data-independent setting where classifiers are represented only by data-independent message...

The Brudnyi-Krugljak theorem on the if-divisibility of Gagliardo couples is derived by elementary means from earlier results of LorentzShimogaki on equimeasurable rearrangements of measurable functions. A slightly stronger form of Calderón's theorem describing the Hardy-LittlewoodPólya relation in terms of substochastic operators (which itself generalizes the classical Hardy-Littlewood-Pólya re...

introduction: landslides are amongst the most damaging geologic hazards in the world. they pose a threat to the safety of humankind lives as well as the environment, resources and property. compared with other natural hazards such as volcanic eruptions and floods, landslides cause considerable damage to human beings and massive economic losses (guzzetti, 2005). according to preliminary estimates...