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Statistica Sinica 16(2006), 459-469





SIGNAL PROBABILITY ESTIMATION WITH PENALIZED

LIKELIHOOD METHOD ON WEIGHTED DATA


Fan Lu, Gary C. Hill, Grace Wahba and Paolo Desiati


University of Wisconsin-Madison


Abstract: In this work we consider the problem faced by astrophysicists where high energy signal neutrinos must be separated from overwhelming background events. We propose a modification to the usual penalized likelihood approach, to take account of the usage of importance sampling techniques in the generation of the simulated training data. Each simulated multivariate data point has two associated weights, which define its contribution to the signal or background count. We wish to find the most powerful decision boundary at a certain significance level to optimally separate signal from background neutrinos. In this modified penalized likelihood method, the estimation of the logit function involves two major optimization steps and the use of KL (Kullback-Leibler) distance criterion for model tuning. We compare this approach with a non-standard SVM (support vector machine) approach. Results on simulated multivariate normal data and simulated neutrino data are presented. For the neutrino data, since the truth is unknown, we show a way to check whether the proposed method is working properly.



Key words and phrases: Kullback-Leiber distance, logit function, neutrino signal, nonstandard support vector machine, penalized likelihood method, simplex method.

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