Mean and variance of ratio estimators used in fluorescence ratio imaging

✍ Scribed by G.M.P. van Kempen; L.J. van Vliet

• Publisher: John Wiley and Sons
• Year: 2000
• Tongue: English
• Weight: 187 KB
• Volume: 39
• Category: Article
• ISSN: 0196-4763
• DOI: 10.1002/(sici)1097-0320(20000401)39:4<300::aid-cyto8>3.0.co;2-o

✦ Synopsis

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.