Method of moments and treatment of nonrandom error.
If one has a convoluted fluorescence decay and wishes to analyze it for a sum of exponential, then one can begin by asking either of two questions: (1) What sum of exponentials best fits the data? (2) What physical decay parameters gave rise to the data? At first these two questions may sound equivalent; in fact, they represent different philosophical approaches to data analysis. In resolving the first question, one adjusts the decay parameters until a calculated curve agrees within arbitrarily chosen limits to the original data. This is what we did in the fourth section of Table II. The fit obtained was decent, but the resulting parameters were wrong. A more difficult approach is to design a method of data analysis which is intrinsically insensitive to the presence of anticipated errors, aiming directly at recovering the decay parameters without regard to the fit. This is what we have done with the method of moments with MD. If particular errors do not have much effect on the recovered parameters, then such a method of data analysis is said to be robust with respect to those errors. Robust methods are widely used in engineering but have not seen much introduction yet to biophysics. Least-squares, the basis of the commonly used data fitting methods for pulse fluorometry, is nonrobust with respect to underlying noise distributions. Isenberg has shown that least-squares is nonrobust with respect to the nonrandom light scatter, time origin shift, and lamp width errors as well. As shown in Isenberg's paper, as well as here, the method of moments with MD is quite robust with respect to these nonrandom errors. Perhaps question (1) could be modified to include all of the errors that might be present in the data; but then, how would one decide which errors to include and whether an error is present? What fitting criterion would tell one this? Why choose a method which depends so strongly on this information when robust alternatives exist? As a rule, fitting should not be used as a criterion for correct decay parameters, unless all of the significant nonrandom errors have been included in the fit. If one fits the data but has not incorporated an important error, then the best fit will necessarily give the wrong answer. The method of moments provides clear criteria for accepting or rejecting an analysis.(ABSTRACT TRUNCATED AT 400 WORDS)
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Department of Chemistry and Biochemistry, Eastern Washington University, Cheney 99004.
D003627:Data Interpretation, Statistical; D007700:Kinetics; D008432:Mathematical Computing; D012984:Software; D013050:Spectrometry, Fluorescence / Q000379:methods*