Hi all,

I am curious to see how to compute SE as in the output of the loo package when we use function waic(.).

I know that from the formula Gelman et al. (2013) we can estimate WAIC using

computed\mbox{ }lppd= \sum\limits_{i=1}^{N}\mbox{log}\left(\frac{1}{S}\sum\limits_{s=1}^{S}p(\boldsymbol{y}_i|\boldsymbol{\eta}^s)\right)

and

\sum_{i=1}^{N}V_s^{S}\left(\mbox{log }p\left(\boldsymbol{y}_i|\boldsymbol{\eta}^s\right)\right)

I think that after running the model, then S is taken as a fixed number (the sampling part). Therefore we can obtain one estimate.

Could anyone help me to understand why we have SE in the output?

Thank you for reading and Happy New Year!