Monte Carlo,hypothesis-tests for rare events superimposed on a background

We describe two techniques to search for small numbers of counts under a peak of known shape and superimposed on a background with statistical fluctuations. Many comparisons of a single experimental spectrum with computer simulations of the peak and background are made. From these we calculate the probability that y hypothesized counts in the peaks of the simulations, will result in a number larger than that observed in a given energy interval (bin) in the experimental spectrum. This is done for many values of the hypothesized number y. One procedure is very similar to testing a statistical hypothesis and can be analytically applied. Another is presented which is related to pattern recognition techniques and is less sensitive to the uncertainty in the mean. Sample applications to double beta decay data are presented.