Bayesian bootstrap for uncertainty estimates

[stan-dev]

Bayesian bootstrap for uncertainty estimates

[jgabry]

@avehtari can we close this now that BB is added in loo 2? Or do you want this as something separate/additional?

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[avehtari]

Let's discuss this next week

[ParadaCarleton]

Unsure how much of this was ever implemented -- if it was, it should probably be emphasized more in the vignettes, since I didn't see anything related to it besides a small mention that it can be used as part of model stacking algorithms. (Although I may have missed it!)

If the Bayesian bootstrap has been added, histospline smoothing may be worth looking at for improving inference with small samples. I'm not 100% sure whether BCa can be extended to the Bayesian bootstrap as well, but if so, that might be interesting to add later on.

[avehtari]

Bayesian bootstrap is used by loo_model_weights() which has documentation with examples.

Based on https://arxiv.org/abs/2008.10296 and related additional experiments, it seems the benefit of Bayesian bootstrap in uncertainty estimate is smaller than what I assumed in 2017 when creating this issue. I close this now. If you are interested in histospline, the discussion related to would be better elsewhere or in a new issue.