\[ \newcommand{\Expect}[1]{\mathbf{E}\left[ #1 \right]} \newcommand{\Var}[1]{\mathrm{Var}\left[ #1 \right]} \newcommand{\Prob}[1]{\mathrm{Pr}\left( #1 \right)} \newcommand{\Probwrt}[2]{\mathrm{Pr}_{#2}\left( #1 \right)} \]

- Knowing the sampling distribution of a statistic tells us about statistical uncertainty (standard errors, biases, confidence sets)
- The bootstrap principle:
*approximate*the sampling distribution by*simulating*from a good model of the data, and treating the simulated data just like the real data - Sometimes we simulate from the model we're estimating (model-based or "parametric" bootstrap)
- Sometimes we simulate by re-sampling the original data (resampling or "nonparametric" bootstrap)
- Stronger assumptions \(\Rightarrow\) less uncertainty
*if we're right*