Decomposition
The Mathematics of Loglet Analysis
The Mathematics of Loglet Analysis
Consider the twodimensional space in which our data set D exists. If
there are m data points, then we define D as
where t_{i} usually represents time, while d_{i} represents the
growing variable (e.g., number of organisms, percent of saturation).
Suppose we want to fit a logistic curve of n components to the model.
Then we will require 3n parameters, represented as a
matrix
,
where the ith row describes the ith component:
Thus a loglet can be alternatively specified by
Figure 5A shows a hypothetical data set
(the circles) and a fitted loglet with n=2 and
Gaussian noise was added to the data to dataset to show the residuals.
Figure 5:
A hypothetical bilogistic data set(A), the residuals of the
fitted curve(B), and the decompositions in raw form (C) and
with the FisherPry transform applied (D).

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Perrin S Meyer
19980714