Don´t subtract the background [signal count analysis method]

When phenomena occur at the threshold of detection capabilities, event rates are low and observers usually record data as discrete counts. In this article, I outline a statistically reliable and efficient method for analyzing signal counts superimposed on background counts that are not subtracted before the data are analyzed. The Poisson statistics of the data are used with a maximum likelihood estimation (MLE) of the parameters. Although I devised the method to improve estimates of yields in low-energy nuclear reactions, it is generally applicable because it is independent of background or signal-shape details. In addition to estimating total signal counts, the analysis produces reliable confidence levels for the estimated signal