Standard error of LOO, WAIC and K-fold

General
1

Dear all,
I don’t get why the standard error of LOO, WAIC and K-fold is defined as:

SE(\hat{elpd}_{loo})= \sqrt{n V_{i=1}^n \hat{elpd}_{loo}^i}

From equation(23) of https://arxiv.org/pdf/1507.04544.pdf. Shouldn’t it be something like:

SE(\hat{elpd}_{loo})= \sqrt{\frac{V_{i=1}^n \hat{elpd}_{loo}^i}{n}}?

But maybe I miss something stupid :( Can you help me?

2

Because \widehat{\mathrm{elpd}}_{\mathrm{loo}} is defined in equation (4) as a sum and not as a mean. After the paper was published, I have realized that it’s difficult to remember equation (4) when looking at the equation (23) which looks similar to something which is commonly used. Thanks for reminding about this. I’ll add this to FAQ I’m just making.

3

ehe I was sure I was missing something. Thank you!!

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