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".