I have a special type of model fitting problem that I am trying to solve in Mathematica. Any insight how to attack it using available tools of Mathematica will be great to hear.
We have a variable $$ H=\{h_k\}, \text{ where } k=1,...,15, $$ and each $h_k$ is a 4-tuple of complex numbers $$ h_k=\{a_j+i b_j\} \text{ where } j=1,...,4 $$ and $a_j,b_j$ are normally distributed real numbers.
Now this $H$ is mapped to a object $P=\{p,c\}$ where $p$ is a permutation of integers $\{2,3,...,16\}$ and $c$ is a real number. Now we seek to find an analytic model $f$ such that $f:H \rightarrow P$. Through a Monte Carlo simulation I have got 50000 data for this map $f$. I am stuck with the question about what kind of analytical model to choose and which fitting procedure will be best if one wants to solve this problem in Mathematica? Hope to hear from you people.