Bayesian Background Estimation

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.