I have a problem and I am really in need of your comments. My problem
can be described as follow.

INPUT: Many sets of observed temporal data with T elements (T is
constant). Each set corresponds to a pair of number of entities and
size, denoted by n and s. For example, if n = 50, s = 1000, and T =
1000, I have one set.

OUTPUT: A statistical model illustrating the observed data. In
addition, that model should be able to predict value of output data
with different pairs of (n, s). It means that if we test n = 60 and s
= 1500, we should have output with same shape as observed data and
appropriate values.

I use a nonlinear regression model with normal distributed error term
and the model has some, e.g. 2 (a, b), coefficients. These
coefficients can be expressed as functions of (n, s) with new
coefficients, however. Therefore, these "mother" coefficients have
"sibling" coefficients. For example, consider coefficient a = f_1(n,
s) = a_1*n + a_2*s; that means a_1 and a_2 are sibling coefficients of
a.

I want to use Markov chain Monte Carlo method to generate values for
these coefficients. In MCMC method, suppose that (a, b) are
multivariate normal distributed, we need a covariance matrix. There
are some studies on this stuff. Nevertheless, the posed situation in
my problem is a little different as it has siblings. Because of this
reason, I do not know how to compute covariance matrix, which needs to
take care of all sibling coefficients, not just 2 mother coefficients.

Could you please kindly recommend me something to do with this
problem?

I would highly appreciate every comment that you can give me. Thank
you very much.