Mean and variance of ratio estimators used in fluorescence ratio imaging

Background: The ratio of two measured fluorescence signals (called x and y) is used in different applications in fluorescence microscopy. Multiple ins tances of both signals can be combined in different ways to construct diffe rent ratio estimators. Methods: The mean and variance of three estimators for the ratio between tw o random variables, x and y, are discussed. Given n samples of x and y, we can intuitively construct two different estimators: the mean of the ratio o f each x and y and the ratio between the mean of x and the mean of y. The f ormer is biased and the latter is only asymptotically unbiased. Using the s tatistical characteristics of this estimator, a third, unbiased estimator c an be constructed. Results: We tested the three estimators on simulated data, real-world fluor escence test images, and comparative genome hybridization (CGH) data. The r esults on the simulated and real-world test images confirm the presented th eory. The CGH experiments show that our new estimator performs better than the existing estimators. Conclusions: We have derived an unbiased ratio estimator that outperforms i ntuitive ratio estimators. Cytometry 39:300-305, 2000. (C) 2000 Wiley-Liss, Inc.