Exchange of Comments on Data Analysis in the Shot Noise Limit Part I: Single Parameter Estimation with Poisson and Normal Probability Density Functions
The first part of this reply to Ron Williams’ comment (I) summarizes and explains in more detail the counting statistics that were used to derive the equations at issue (2). A review of this material is necessary in order to point out some of the fundamental implications of the equations derived in ref 2. In the second part, an explanation of the error in ref 1 will be used to illustrate a problem in interpretation of analog data with formulas derived from counting statistics. In essence, the maximum likelihood estimator equation derived in ref 2 was incorrectly applied by not accounting for the conversion between photon counts and photomultiplier current.
Exchange of Comments on Data Analysis in the Shot Noise Limit Part I: Single Parameter Estimation with Poisson and Normal Probability Density Functions Stephen E. Bialkowski Analytical Chemistry 62 2141 1990