best strategy to fit the given function to my data

*To*: mathgroup at smc.vnet.net*Subject*: [mg71183] best strategy to fit the given function to my data*From*: aitor69gonzalez at gmail.com*Date*: Fri, 10 Nov 2006 06:37:35 -0500 (EST)

Hello, I have a set of data that can be approximated by the 2-variable function "noisydyn[a_,t_]". The function "noisydyn[a_,t_]" contains a Sin function, because there is oscillation in my data, and a Step (Heaviside) function, because the observations are Boolean. The function "noisydyn[a_,t_]" also contains a sigmoid (Hill) function, "Period[a_]" with three unknown parameters, "m", "theta" and "T" that I have approximated to the data by hand. (*Remove["Global`*"]; Off[General::spell1];*) m = 4; theta = 2400; T = 120; Period[a_] := T*(1 + 11*(a^m/(a^m + theta^m))); noisydyn[a_, t_] := UnitStep[Sin[ 2*\[Pi]*((t - a)/T + a/Period[a]) - Random[Real, {-0.5, 0.5}]]]; data = Table[noisydyn[a, t], {a, 0, 720, 20}, {t, 0, 120, 2}]; ListDensityPlot[data, Mesh -> False]; I have found in Mathematica several functions to fit data, Nminimize, Nmaximize, Fit, etc, but I do not know, which of them should I use. Given the functions "Period" and "noisydyn", how I can fit the parameters "m", "theta" and "T" to the Table "data". Thank you in advance, Aitor

**Follow-Ups**:**Re: best strategy to fit the given function to my data***From:*Christopher Arthur <caa0012@unt.edu>