In gbonte/gbcode: Code from the handbook "Statistical foundations of machine learning"

Shiny dashboard "Statistical foundations of machine learning"

Bootstrap

Goal: show that bootstrap is an effective resampling strategy to approximate the sampling distribution of the estimators

Common left panel:

• Number of samples: number of samples of observed dataset
• Number of MC trials: number of Monte Carlo trials used to simulate the data generating process
• Number of bootstrap repetitions: number of resampling repetitions with replacement

point estimation (1D Gaussian)

Data generating process: normal random variable ${\bf z} \sim {\mathcal N} (\mu,\sigma^2)$. Estimation of mean and variance.

• Slider $\mu$: mean parameter
• Slider $\sigma^2$: variance parameter
• Top right panel: visualization of density probability and sampled dataset
• Center left panel: MC sampling distribution of the estimator of the mean (including the estimator's mean and variance)
• Center right panel: MC sampling distribution of the estimator of the variance (including the estimator's mean and variance)
• Bottom left panel: bootstrap approximation of sampling distribution of the estimator of the mean (including the bootstrap estimation of estimator's bias and variance)
• Center right panel: bootstrap approximation of sampling distribution of the estimator of the variance (including the bootstrap estimation of estimator's bias and variance)

Suggested manipulations:

• change $\sigma^2$ and see the impact on the accuracy of the bias/variance bootstrap estimation
• change the number of bootstrap samples and see the impact on the accuracy of the bias/variance bootstrap estimation
• change number of MC trials and see that it affects only the center panels
• change number of bootstrap repetitions and see that it affects only the bottom panels

gbonte/gbcode documentation built on Feb. 27, 2024, 7:38 a.m.