Schedule
Classes normally meet Tuesdays and Thursdays at 10:00 AM in PH 109.
This schedule is provisional and will be updated as topics, assignments, holidays, and examination details are finalized.
August
| Week | Date | Topic | Slides / Materials |
|---|---|---|---|
| 1 | Tue Aug 18 | Introduction; Monte Carlo for uncertainty; Travel-time simulation | Introduction |
| Thu Aug 20 | Probability review; Sampling schemes; Bias, variance, and confidence intervals; Estimators and estimates | Introduction | |
| Fri Aug 21 | Diagnostic Survey due | Assignment 0 — Diagnostic Survey | |
| 2 | Tue Aug 25 | Conditional Monte Carlo and low discrepancy examples; Quantile transforms | Introduction Generating Samples |
| Thu Aug 27 | Conditional Monte Carlo review; Mixture sampling; Multivariate normal and Cholesky sampling; Gaussian-process introduction | Introduction Generating Samples |
September
| Week | Date | Topic | Slides / Materials |
|---|---|---|---|
| 3 | Tue Sep 1 | Gaussian processes and Brownian motion; Cholesky and PCA factorizations; Geometric Brownian motion and option pricing; Low discrepancy comparison | Introduction Generating Samples |
| Wed Sep 2 | Assignment 1 due | Owen Exercises 1.2 and 2.1 | |
| Thu Sep 3 | Transport maps; Acceptance–rejection sampling and its justification; Gaussian-mixture low discrepancy comparison | Generating Samples | |
| 4 | Tue Sep 8 | Unit-cube integration and transformation smoothness; Metropolis–Hastings sampling; Proposal tuning, burn-in, and separated modes | Generating Samples Markov Chain Monte Carlo |
| Thu Sep 10 | MCMC tuning and diagnostics; Parallel-tempering introduction; Kernel discrepancy for distributions and samples; Kernel scale and sample-quality comparisons | Markov Chain Monte Carlo | |
| Fri Sep 11 | Assignment 2 due | Owen Exercises 4.5 and 4.19 | |
| 5 | Tue Sep 15 | Test 1 | Covers Introduction Generating Samples |
| Thu Sep 17 | Unit-cube sampling review; Unbiased squared-discrepancy estimates; RKHS worst-case integration error; Gaussian-process RMSE and kernel assumptions | Generating Samples Markov Chain Monte Carlo |
|
| Fri Sep 18 | Project topic submission deadline | Topic Selection & Presentation Scheduling | |
| 6 | Tue Sep 22 | Centered discrepancy and smoothness; brief KL and Stein comparisons; likelihood and Bayesian inference; mixture-posterior MCMC and parallel tempering; queueing preview | Markov Chain Monte Carlo Bayesian MCMC notebook |
| Thu Sep 24 | Queue state and residual clocks; next-event updates and Markov interpretation; worked queue example and three group exercises; time in system and stopping rule | Markov Chain Monte Carlo | |
| Fri Sep 25 | Assignment 3 due | Owen Exercises 5.4 and 5.13 | |
| 7 | Tue Sep 29 | Queue-simulation recap and notebook; MCMC synthesis; variance and variation reduction, Keister transformations, and importance sampling through “Variance depends on the function” | Markov Chain Monte Carlo Queue simulation notebook Improving Efficiency |
October
| Week | Date | Topic | Slides / Materials |
|---|---|---|---|
| 7 | Thu Oct 1 | Brownian motion with drift and choosing a transformation; control variates, least-squares coefficients, and practical control choices; Asian-option notebook walkthrough | Improving Efficiency Asian-option notebook |
| 8 | Tue Oct 6 | Control-variate recap; conditional Monte Carlo; conditional density estimation for sums of uniforms and Asian averages; Asian-call payoff distribution | Improving Efficiency Conditional Monte Carlo notebook |
| Wed Oct 7 | Assignment 4 due | Owen Exercises 11.5 and 11.6 | |
| Thu Oct 8 | Transformation and control-variate cost comparisons; antithetic sampling and variance derivation; IID Asian/lookback comparison; introduction to the van der Corput sequence | Improving Efficiency Asian-option notebook |
|
| Mon Oct 12 | Midterm course evaluation due |
Complete in Canvas or use your invitation email |
|
| 9 | Tue Oct 13 | No Class — Fall Break | |
| Thu Oct 15 | Recap van der Corput; resume at “Four low discrepancy families”; return to the deferred Asian-option variance/time interpretation | Improving Efficiency Asian-option notebook |
|
| 10 | Tue Oct 20 | ||
| Wed Oct 21 | Assignment 5 due | Details TBD | |
| Thu Oct 22 | |||
| 11 | Tue Oct 27 | Test 2 | Coverage TBD |
| Thu Oct 29 |
November
| Week | Date | Topic | Slides / Materials |
|---|---|---|---|
| 12 | Tue Nov 3 | ||
| Thu Nov 5 | |||
| 13 | Tue Nov 10 | ||
| Thu Nov 12 | |||
| Fri Nov 13 | Assignment 6 due | Details TBD | |
| 14 | Tue Nov 17 | ||
| Thu Nov 19 | |||
| 15 | Mon Nov 23 | Project presentations | Project information |
| Tue Nov 24 | Project presentations | Project information | |
| Thu Nov 26 | No Class — Thanksgiving holiday |
December
| Week | Date | Topic | Slides / Materials |
|---|---|---|---|
| 16 | Tue Dec 1 | ||
| Thu Dec 3 |
The official last day of classes is Saturday, December 5. Because the course meets on Tuesdays and Thursdays, Thursday, December 3 is the final regular class meeting.
Final examinations
Final examinations occur during the following week.
| Week | Date | Topic | Slides / Materials |
|---|---|---|---|
| 17 | TBA | Final Exam — time and location TBA | Whole course; greater emphasis on material not covered by Test 1 or Test 2 |