title: Mean and variance of ratio estimators used in fluorescence ratio imaging.
abstract: 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.
authors.affiliation: Central Analytical Sciences, Unilever Research Vlaardingen, Vlaardingen, The Netherlands. geert-van.kempen@unilever.com
authors.forename: G M
authors.initials: GM
authors.lastname: van Kempen
authors.forename: L J
authors.initials: LJ
authors.lastname: van Vliet
mesh_terms: D000704:Analysis of Variance; D003198:Computer Simulation; D005456:Fluorescent Dyes / Q000032:analysis*; D018628:Gene Dosage; D007091:Image Processing, Computer-Assisted / Q000379:methods / Q000706:statistics & numerical data; D008856:Microscopy, Fluorescence / Q000379:methods / Q000706:statistics & numerical data; D016011:Normal Distribution; D009693:Nucleic Acid Hybridization; D016012:Poisson Distribution
chemical_list: D005456:Fluorescent Dyes