Is it the right way to get the prior?

Modeling
1

Dear Stan’s developer:
I would like to define the right prior,is it possible for me to use the idea of “system identification”?
Trying to fit the force curve by gamma distribution.And hope to get a set of proper alpha and gamma!
Below is my model.

stan_model = “”"
data {
int N ; // Number of training samples
int M ;
real force [M,N] ;
}
parameters {
real<lower=0> alpha[M];
real<lower=0> beta[M];
}
model {
for(m in 1:M){
force[m]~ gamma(alpha[m],beta[m]);
}
}
“”"

Any comment would help,thanks!
Eric