Part IX — Monte Carlo Methods¶
Computing with randomness: generating random numbers, sampling from distributions, estimating expectations by simulation, and the variance-reduction and resampling techniques (bootstrap, jackknife) that make simulation estimates usable.
Topics¶
| Topic | Focus |
|---|---|
| Random Number Generation | Pseudorandom generators and seeding |
| Sampling Methods | Inverse-transform and related recipes for sampling from a distribution |
| Monte Carlo Simulation | Estimating expectations by simulation, with error rates |
| Importance Sampling | Reweighting samples from a proposal distribution |
| Rejection Sampling | Accept–reject sampling from an envelope distribution |
| Variance Reduction | Antithetic variates, control variates, and stratification |
| Bootstrap Methods | Resampling the data to approximate sampling distributions |
| Jackknife Methods | Leave-one-out resampling for bias and variance estimates |