I am new to Bayesian statistics, and thus have problems to come up with a solution for the following problem:
Using Approximate Bayesian Computation (ABC), I generate a posterior distribution from one set of observed summary statistics, and a set of about a million simulated summary statistics. The prior distribution is the variable value of the model parameter used in the simulations. The posterior distribution is used to obtain point estimates (e.g., mode, mean, etc.) of the underlying model parameter.
The biological problem I am working on is that the true parameter value cannot be estimated from one observation only. Hence, I have N observed data sets, and obtain N posterior distributions. In ABC, I use the same simulated data for each observation data set.
Now, my problem is to combine the N posterior distributions in a way to estimate the true parameter value, thus capturing the information contained in all N densities.