Math 577 -- Monte Carlo Methods

Spring 2026

Calendar

* [2026-05-11 Mon] 1-3p: presentations
* [2026-05-06 Wed] TBA
* [2026-05-04 Mon] TBA
* [2026-05-01 Fri] makeup class (usual time)
* [2026-04-29 Wed] no class
* [2026-04-27 Mon] no class
* [2026-04-22 Wed] TBA
* [2026-04-20 Mon] TBA
* [2026-04-15 Wed] HMC
* [2026-04-13 Mon] HMC
- Hamiltonian Monte Carlo
* [2026-04-08 Wed] MALA; HMC
- Metrolis Adjusted LAngevin sampling
- intro to Hamiltonian Monte Carlo
* [2026-04-06 Mon] continuous MCMC; Langevin sampling
* [2026-04-01 Wed] Burn in diagnostics; Metropolis in continuous spaces
- estimating exponential autocorrelation time
- Gelman-Rubin
- references: mc11a, mc11c
* [2026-03-30 Mon] Error analysis (empirical)
- estimating IACT
- batch means
- references: mc11a, mc11b
* [2026-03-25 Wed] Error analysis: from theory to practice
- more on Kubo formula
- estimating IACT
- references: mc11a
* [2026-03-23 Mon] Error analysis (theory)
- Kubo formula
- reference: mc11
* [2026-03-18 Wed] Metropolis algorithm
- more on Metrpolis
- Ising model
- reference: mc10a
* [2026-03-16 Mon] Markov chain Monte Carlo
- reversibility and spectral theorem
- Metropolis algorithm
- reference: mc10a
* [2026-03-04 Wed] Markov chains
- finite state Markov chains: basic theory and definitions
- reversible chains and detailed balance
- Perron-Frobenius Theorem
- reference: mc10
* [2026-03-02 Mon] Cramer's theorem & rare events for random walks
- proof of Cramer's theorem
- rare events for random walks: Siegmund's algorithm
- reference: mc09a, mc09b
* [2026-02-25 Wed] more on rare events
- bounded relative error
- log efficiency
- reference: mc09, mc09a
* [2026-02-23 Mon] importance sampling & rare events
- basic example of rare event simulation
- references: mc08c, mc09
* [2026-02-18 Wed] variance reduction
- importance sampling
- optimal biasing distribution
- rare events
- references: mc08, mc08a, mc08b, mc08c
* [2026-02-16 Mon] weighted samplers; variance reduction
- weighted samplers
- general intro to variance reduction
- antithetic variates
- control variates
- references: mc07, mc08
* [2026-02-11 Wed] stationary gaussian processes; rejection sampling
- references: mc06
* [2026-02-09 Mon] stationary gaussian processes
- references: mc05b
* [2026-02-04 Wed] circulant matrices
- references: mc05a
* [2026-02-02 Mon] more gaussians
- references: mc05
* [2026-01-28 Wed] gaussians
- multidimensional transform methods
- Box-Mueller for independent standard normals
- affine transforms for multidimensional gaussians
- reference: mc04, mc05
* [2026-01-26 Mon] transformation methods
- reference: mc04
* [2026-01-21 Wed] intro to sampling
- mc integration
- "random" numbers
- cdf transform
- reference: mc02, mc03
* [2028-01-14 Fri] admin & intro
- administrivia
- example: estimating pi
  - 2d
  - higher dimensions
- estimator variance
- comparison to deterministic "quadrature"
- reference: mc01