Analysis of multicomponent mass spectra applying Bayesian probability theory.

In this paper we develop a method for the decomposition of mass spectra of gas mixtures, together with the relevant calibration measurements. The method is based on Bayesian probability theory. Given a set of spectra, the algorithm returns the relative concentrations and the associated margin of confidence for each component of the mixture. In addition to the concentrations, such a data set enables the derivation of improved values of the cracking coefficients of all contributing species, even for those components for which the set does not contain a calibration measurement. This latter feature also allows one to analyze mixtures that contain radicals in addition to stable molecules. As an example, we analyze and discuss the mass spectra obtained from the pyrolysis of azomethane, which contain the radical CH3 apart from nitrogen and C1- and C2-hydrocarbons.

Simulations on infinite-size lattices.

We introduce a Monte Carlo method, as a modification of existing cluster algorithms, which allows simulations directly on systems of infinite size, and for quantum models also at beta = infinity. All two-point functions can be obtained, including dynamical information. When the number of iterations is increased, correlation functions at larger distances become available. Limits q-->0 and omega-->0 can be approached directly. As examples we calculate spectra for the d = 2 Ising model and for Heisenberg quantum spin ladders with two and four legs.

Background estimation in experimental spectra

A general probabilistic technique for estimating background contributions to measured spectra is presented. A Bayesian model is used to capture the defining characteristics of the problem, namely, that the background is smoother than the signal. The signal is allowed to have positive and/or negative components. The background is represented in terms of a cubic spline basis. A variable degree of smoothness of the background is attained by allowing the number of knots and the knot positions to be adaptively chosen on the basis of the data. The fully Bayesian approach taken provides a natural way to handle knot adaptivity and allows uncertainties in the background to be estimated. Our technique is demonstrated on a particle induced x-ray emission spectrum from a geological sample and an Auger spectrum from iron, which contains signals with both positive and negative components.

Signal and background separation.

In many areas of research the measured spectra consist of a collection of "peaks"--the sought-for signals--which sit on top of an unknown background. The subtraction of the background in a spectrum has been the subject of many investigations and different techniques, varying from filtering to fitting polynomial functions, have been developed. These techniques yield results that are not always satisfactory and often even misleading. Based upon the rules of probability theory, we derive a formalism to separate the background from the signal part of a spectrum in a rigorous and self-consistent manner. We compare the results of the probabilistic approach to those obtained by two commonly used methods in an analysis of particle induced x-ray emission spectra.

Reconstruction of surfaces from phase-shifting speckle interferometry: Bayesian approach.

The reconstruction of surfaces from speckle interferometry data is a demanding data-analysis task that involves edge detection, edge completion, and image reconstruction from noisy data. We present an approach that makes optimal use of the experimental information to minimize the hampering influence of the noise. The experimental data are then analyzed with a combination of wavelet transform and Bayesian probability theory. Nontrivial examples are presented to illustrate the proposed technique.