One major challenge with the modelisation of complex problems using Markov chain Monte Carlo (MCMC) methods is the determination of the length of the chain in order to reach convergence. This paper is devoted to parametric empirical methods testing the stationarity. We compare the methods of...

Given a countable structure , we define the degree spectrum of to be the set of all enumeration degrees generated by the presentations of on the natural numbers. The co-spectrum of is the set of all lower bounds of . We prove some general properties of the degree spectra which show that they...

Dual scattering channel schemes extend the transmission line matrix numerical method (J' TLM algorithm) in two directions. For one point, transmission line links are replaced by abstract scattering channels in terms of paired distributions (characteristic impedances are thus neither needed, nor...

The partial attributable risk has been introduced as a tool for partitioning the responsibility for causing an adverse event between various risk factors. It has arisen from epidemiology but is also a valid general risk allocation concept which can for example be applied to data from customer...

Stein's Lemma, important in statistics and also in capital asset pricing models, is generalized to the case of elliptical class of distributions. The case when the covariance matrix of the underlying distribution does not exist, is also considered. The results are illustrated by multivariate...

Hypernormal forms (unique normal forms, simplest normal forms) are investigated both from the standpoint of foundational theory and algorithms suitable for use with computer algebra. The Baider theory of the Campbell-Hausdorff group is refined, by a study of its subgroups, to determine the...

The common probabilities of two or more semantically independent hypotheses or series of observation, supporting one another, may be calculated by the MPE-Method (Multiplication of the probabilities of error and subtraction of the product from 1.0, Gottlob, 2000). Here, I prove that by the...

The common probabilities of two or more semantically independent hypotheses or series of observation, supporting one another, may be calculated by the MPE-Method (Multiplication of the probabilities of error and subtraction of the product from 1.0, Gottlob, 2000). Here, I prove that by the...