Concerning model evaluation, if you are interested in checking the “absolute” fit of your model to the data, you can do the following:
- choose a checking function to analyse the discrepancy between your model and the data;
- plot the (prior and/or posterior) predictive distribution of this checking function;
- check if the observed value of the checking function is located in a high distribution region and not in the tails of the distribution.
Still concerning model evaluation, you can choose a checking function that depends on the parameters of the model. Given a set of draws from the posterior distribution of the parameters conditional on the data (Markov Chain Monte Carlo - Metropolis_Hasting), you can go like this:
for each parameter draw, simulate the model to get a replicated data from the sampling distribution of the observables conditional on the parameter;
compute two values of the checking function: one with the data and the other with the replicated data;
repeat the above steps for all parameter draws and make a two-dimensional scatter plot with all pairs of checking function values;
check if the proportion of points above the 45º line is about 50%.