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30 The Bootstrap and Bagging

The bootstrap is a technique for approximately sampling from the error distribution for an estimator. Thus it can be used as a Monte Carlo method to estimate standard errors and confidence intervals for point estimates (Efron and Tibshirani 1986, 1994). It works by subsampling the original data and computing sample estimates from the subsample. Like other Monte Carlo methods, the bootstrap is plug-and-play, allowing great flexibility in both model choice and estimator.

Bagging is a technique for combining bootstrapped estimators for model criticism and more robust inference (Breiman 1996; Huggins and Miller 2019).


Breiman, Leo. 1996. “Bagging Predictors.” Machine Learning 24 (2): 123–40.

Efron, Bradley, and Robert Tibshirani. 1986. “Bootstrap Methods for Standard Errors, Confidence Intervals, and Other Measures of Statistical Accuracy.” Statistical Science 1 (1): 54–75.

Efron, Bradley, and Robert J Tibshirani. 1994. An Introduction to the Bootstrap. Chapman & Hall/CRC.

Huggins, Jonathan H, and Jeffrey W Miller. 2019. “Using Bagged Posteriors for Robust Inference and Model Criticism.” arXiv, no. 1912.07104.