- #1

yumyumyum

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a) to use the jacobian to linearize, and proceed with linear regression, or to

b) linearize the raw data

2) When data needs to be "fit" to a complicated model (e.g. some non-linear differential equation) that has no closed form analytic solution, people typically run a simulation varying the model parameters until the least squares residuals is minimized. Fit parameter distributions are then estimated using monte carlo boostrap, or a polynomial approximation in the vicinity of the residual least squares minimum.

Has anyone here seen any literature about linearizing the data for case 2 and fitting with a difference equation approximation for the non-linear dif. e.q. ? For example let's say our data is described by y = A*exp(-t/tau)+c. The y data can be linearized by with a time difference approximation

y(t+1)-y(t)/dt = -y(t)/tau.

and the equation above can be use to fit it. This technique would also apply to more complicated non-linear diffy q's so long they can represented as difference equations.