How to pool Bayesian R-Squared values in multiple imputation?

I am running a multilevel model in multiple imputed datasets (from {mice}) using brm_multiple(). I would like to report the Bayesian R^2 value for the model but am not sure the best way to pool it. I could see reporting the distribution of R^2 values across imputed datasets, but I imagine there might be a better way to proceed. Any suggestions? Thanks!

For some parameters, like slopes and intercepts, it seems that simply combining the posterior samples across datasets is sufficient for pooling. But for others, like \hat{R} and ESS, it is better to look at them for each dataset separately. So I’m just not sure which camp R^2 would fall into.

First one for Bayesian R^2.

Perfect! That makes my life easier. Thanks, Aki.