Maximum Entropy and Bayesian Methods, J. T. Rychert, G. J. Erickson, and C. R. Smith, eds., AIP Conf. Proc. 568, pp. 604-614 (AIP, Melville, NY, 2001)

Background estimation in experimental spectra

R. Fischer (1), K. M. Hanson (2), V. Dose (1), and W. von der Linden (3)
(1) Max Planck Institute for Plasma Physics, (2) Los Alamos National Laboratory, and (3) Institutes for Theoretical Physics, University of Graz


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 PIXE spectrum from a geological sample and an Auger spectrum from iron, which contains signals with both positive and negative components.

Keywords: background estimation, Bayesian analysis, outliers, PIXE spectra, Auger spectra

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