Marginalization using the metric of the likelihood

Although the likelihood function is normalizeable with respect to the data there is no guarantee that the same holds with respect to the model parameters. This may lead to singularities in the expectation value integral of these parameters, especially if the prior information is not sufficient to take care of finite integral values. However, the problem may be solved by obeying the correct Riemannian metric imposed by the likelihood. This will be demonstrated for the example of the electron temperature evaluation in hydrogen plasmas.Comment: 8 pages, 2 figures, Presented at the MaxEnt 2000 conference in Gif-sur-Yvette/Pari

Bayesian analysis of magnetic island dynamics

We examine a first order differential equation with respect to time coming up in the description of magnetic islands in magnetically confined plasmas. The free parameters of this equation are obtained by employing Bayesian probability theory. Additionally a typical Bayesian change point is solved in the process of obtaining the data.Comment: 10 pages, 4 figures, submitted to be included in MaxEnt 2002 proceeding

Decomposition of multicomponent mass spectra using Bayesian probability theory

We present a method for the decomposition of mass spectra of mixture gases using Bayesian probability theory. The method works without any calibration measurement and therefore applies also to the analysis of spectra containing unstable species. For the example of mixtures of three different hydrocarbon gases the algorithm provides concentrations and cracking coefficients of each mixture component as well as their confidence intervals. The amount of information needed to obtain reliable results and its relation to the accuracy of our analysis are discussed