Bootstrap
Shuffling reality to produce your data
2014-11-26 — 2022-01-27
Resampling your own data to estimate how good your point estimator is and to reduce its bias. In general, it’s an intuitive technique. However, it gets tricky for, e.g., dependent data. For a handy crib sheet for bootstrap failure modes, see Thomas Lumley, When the bootstrap doesn’t work.
In the classical mode, this is a frequentist technique without an immediate Bayesian interpretation.
Commonly credited to B. Efron (1979) and theoretically justified by Gine and Zinn (1990).
1 Teaching
2 Bootstrap bias correction
As opposed to variance estimation. NBD; Bootstrap is notionally telling you the sampling distribution. 🏗
3 Bootstrap for dependent data
e.g., as presaged, time series. Parametric bootstrap would be the logical default choice, right? When does that work?
4 Causal bootstrap
Now a thing! (Imbens and Menzel 2021)
5 As a Bayesian method
There is absolutely a Bayesian bootstrap if you think hard enough about it, it turns out. Several, really. Rubin (1981) derived a Bayesian version. See Lyddon, Holmes, and Walker (2019) for a modern update, and Rasmus Bååth for a diagrammed explanation of the points of contact with frequentist bootstrap and some other things.
6 Pedagogic
Tim Hesterberg’s teaching notes:
7 References
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———. 2012. “Bayesian Inference and the Parametric Bootstrap.” The Annals of Applied Statistics.
———. 2021. “Resampling Plans and the Estimation of Prediction Error.” Stats.
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