Numerical Computer Methods, Part C, Volume 321 (Methods in by John N. Abelson, Melvin I. Simon, Michael L. Johnson, Ludwig

By John N. Abelson, Melvin I. Simon, Michael L. Johnson, Ludwig Brand

The seriously acclaimed laboratory ordinary for greater than 40 years, Methods in Enzymology is likely one of the so much hugely revered courses within the box of biochemistry. seeing that 1955, every one quantity has been eagerly awaited, often consulted, and praised through researchers and reviewers alike. Now with greater than three hundred volumes (all of them nonetheless in print), the sequence includes a lot fabric nonetheless suitable today--truly a necessary book for researchers in all fields of existence sciences.

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The cross-correlation coefficient 17 D. W. Marquardt, S1AMJ. Appl. Math 14, 1176 (1963). 18 p. R. Bevington, "Data Reduction and Error Analysis for the Physical Sciences," p. 246. McGraw-Hill, New York, 1969. ,k - 1 1/2 [(A A)j,j- I (A T A)Lk] (25) T The values of the cross-correlation coefficients range from minus to plus one. , can be independently determined), their cross-correlation coefficients are zero. Conversely, the larger the magnitude of the cross-correlation coefficients, the more difficult will be the parameter-estimation process.

This method, too, is quite precise but also requires substantial computer time. An example of the grid search method for the evaluation of confidence intervals is shown in Fig. 3. Thirty synthetic data points were generated 23 j. Beechem, this volume [2]. [l] P A R A M E T E R ESTIMATION BY LEAST-SQUARES 23 to represent a single exponential decay of the type defined by Eq. (1). 5. 0. 1 standard deviation was added to these synthetic data. 3. The baseline was held constant so the graph would contain only two dimensions.

20 The Nelder-Mead algorithm is independent of the number N of data points. However, for statistical significance of the results, there must be a sufficient number of data points for the number M of parameters and the particular fitting function chosen. l 1] PARAMETER ESTIMATION BY LEAST-SQUARES 1 ~_~' Pi 19 (27) where the prime on the summation indicates the specific exclusion of the vertex ph. In general, the procedure proceeds iteratively in three sequential steps: reflection, expansion, and contraction.

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