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Mean and variance of ratio estimators used in fluorescence ratio imaging
G M van Kempen1, L J van Vliet
1Central Analytical Sciences, Unilever Research Vlaardingen, Vlaardingen, The Netherlands. geert-van.kempen@unilever.com
Background:
The ratio of two measured fluorescence signals (called x and y) is used in different applications in fluorescence microscopy. Multiple instances of both signals can be combined in different ways to construct different ratio estimators.
Methods:
The mean and variance of three estimators for the ratio between two 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 of each x and y and the ratio between the mean of x and the mean of y. The former is biased and the latter is only asymptotically unbiased. Using the statistical characteristics of this estimator, a third, unbiased estimator can be constructed.
Results:
We tested the three estimators on simulated data, real-world fluorescence test images, and comparative genome hybridization (CGH) data. The results on the simulated and real-world test images confirm the presented theory. The CGH experiments show that our new estimator performs better than the existing estimators.
Conclusions:
We have derived an unbiased ratio estimator that outperforms intuitive ratio estimators.