I am fit several bayesian models for each individual participant but hope to calculate the overall performance of the model. Right now, I have WAIC for each individual subject for each model, but I am not sure how to get the overall WAIC. Can I just simply sum up the individual WAIC values? or I need to do some more complicated things for the calculation.

I found a reference of computing overall BIC when fitting the model individually in my area(cognitive psychology). For computing overall BIC, the authors use the total number of observations and total number of participants for the calculation.

Are you using R or Python or something else? Which Stan interface? I’m asking as there are packages that could make the computations and diagnostics for you.

Separate model or common model for all subjects? Do you have several observations per subject? How are you computing observation or subject level likelihood and WAIC?

Note also that WAIC is asymptotically equivalent to LOO, but PSIS-LOO has better diagnostic to check when the computation given posterior draws is reliable.