Bayesian background estimation

Abstract

Abstract. The ubiquitous problem of estimating the background of a measured spectrum is solved with Bayesian probability theory. A mixture model is used to capture the defining characteristics of the problem, namely that the background is smoother than the signal. The smoothness property is quantified in terms of a cubic spline basis where a variable degree of smoothness 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, allows uncertainties in the background to be estimated and data points to be classified in groups containing only background and groups with additional signal contribution. Our technique is demonstrated on a PIXE spectrum from a geological sample and an Auger spectrum from an 10 monolayer iron film on tungsten.

Investigation of Selected Baseline Removal Techniques as Candidates for Automated Implementation

“…Methods not described here include those based on principal component analysis or singular value decomposition [69][70][71][72] and Bayesian methods. 65,[73][74][75][76][77] Also not included were methods primarily aimed at mixture resolution and calibration. 12,14,26,28,32,35,37,43,44,47,67,75,[77][78][79][80][81][82] The latter methods often require information about the signal s and involve the resolution of background and signal components through modeling.…”

“…113 It should also be noted that Bayesian methods are in some respects related to MEMs. 65,[73][74][75][76][77] Theory. Durman and Wood 113 model the data as in Eq.…”

Acceleration of Bayesian model based data analysis

“…Increasingly used for different data analysis schemes, one of the currently most transcendent techniques in parameter estimation is Bayesian analysis [5,6,7,8]. It provides a good way to deal with combinations of data from diagnostics measuring the similar parameters.…”