Estimating small signals by using maximum likelihood and Poisson statistics

Estimation of small signals from counting experiments with backgrounds larger than signals is solved using maximum likelihood estimation for situations in which both signal and background statistics are Poissonian. Confidence levels are discussed, and Poisson, Gauss and least-squares fitting methods are compared. Efficient algorithms that estimate signal strengths and confidence levels are devised for computer implementation. Examples from simulated data and a low count rate experiment in nuclear physics are given.