Counting of obscure events: A Bayesian approach

A general method for counting of obscure events in presence of detection noise is presented. The method combines the measurement data with additional information about the system under investigation to improve the measurement accuracy with the help of probability theory. As an example, we apply the method to the case of counting molecules in a microfluidic device and show in simulations that the accuracy is always better than for a thresholding approach. As a second example, we show how it can be used for photon counting at high count rates with an electron multiplying CCD (EMCCD) camera.