| Week | Dates | Lecture Topics | Reading & Presentations |
|---|---|---|---|
| 1 | Jan 16 18 |
Course overview; presentation schedule sign-up Review of MC integration; variance reduction |
Background reading in Ripley, Robert & Casella |
| 2 | Jan 23 25 |
Quadrature vs MC integration Gauss-Hermite Convergence theory of Markov chains in general state spaces |
Evans & Schwartz (1995) Naylor & Smith (1982) (Jarad Niemi) Tierney (1994) (w/ disc) Roberts & Rosenthal (2004) Jones & Hobert (2001) |
| Advanced MCMC | |||
| 3 | Jan 30 Feb 1 |
Rapidly mixing Markov chains, randomized algorithms Output analysis and efficiency Convergence diagnostics Quasi MC |
Aldous (1993),
Jerrum & Sinclair (1996) Randall (2003), Randall (2006) Gelman & Rubin (1992), Cowles & Carlin (1996) Fan, Brooks & Gelman (2005) Ostland & Yu (1997) (James Scott) |
| 4 | Feb 6 8 |
Tempering and annealing algorithms Parallel tempering & applications Auxiliary variable methods: Swendsen-Wang, Wolffe |
Kirkpatrick (1983), Geman & Geman (1984) Geyer & Thompson (1995), Geyer (1991) Cooke & Schmidler (2006) Higdon (1998) (Jeff Sipe) Edwards & Sokal (1989) |
| 5 | Feb 13 15 |
Evolutionary MCMC Slice Sampling Reversible jump |
Liang & Wong (2000) Liang & Wong (2001) (Melanie Wilson) Chen & Schmeiser (1998) (Hao Chen) Neal (2003) (w/ disc) Roberts & Rosenthal (1999) Green (1995) (Josh Robinson) Sisson (2005) |
| Convergence rates for Markov chain simulations | |||
| 6 | Feb 20 22 |
Convergence bounds for finite Markov chains |
|
| 7 | Feb 27 Mar 1 |
General state space Markov chains |
Roberts
& Rosenthal (1997) |
| 8 | Mar 6 8 |
CS Dept Colloquium |
Project proposals due |
| 9 | Mar 13 15 |
Spring break |
|
| 10 | Mar 20 22 |
Parameterization issues MC Optimization |
Gelfand (1995) Geyer & Thompson (1992) Geyer & Thompson (1995) |
| 11 | Mar 27 29 |
Computing normalizing constants |
Gelman & Meng (1998)
Sinharay & Stern (2005)
Raftery & Newton (2006) |
| 12 | Apr 3 5 |
No class. Regeneration; Adaptive MCMC |
Sinharay & Stern (2005) (Joyee Ghosh) Brockwell & Kadane (2004) Roberts & Rosenthal (2006) (Chunlin Ji) Andrieu & Moulines (2005) |
| Dirichlet process models | |||
| Variational methods | |||
| 13 | Apr 10 12 |
Dirichlet process mixtures Variational inference MCMC and variational inference for Dirichlet process mixtures |
Escobar & West (1995) Jaakkola & Jordan (2000) Blei & Jordan (2000) MacEachern & Muller (1998) (Kai Mao) Neal (2000) Blei, Ng & Jordan (2003) (Chunping Wang) |
14 | Apr 17 |
© 2007 Scott C. Schmidler