Master's Thesis from the year 2013 in the subject Mathematics - Stochastics, grade: 1.3, University of Göttingen (Institut für Mathematische Stochastik), language: English, abstract: The present thesis is devoted to the problem of detecting a signal with an unknown spatial extent against a noisy background. This is modelled within the framework of Gaussian mean regression. We compare performances of the maximum likelihood ratio (scan) statistic, the average likelihood ratio statistic and penalized scan statistic in detecting a signal with both unknown amplitude and length. The work contains theoretical as well es application results.