Statistics 8701 (Geyer, Spring 2003) Projects
The following is the list of possible class projects that was discussed
in class.
- Programming.
- Improve the
metropolis function
adding features (such as doing MALA, Metropolis-Adjusted Langevin Algorithm)
or making more usable in other ways (add batching, add user-written functional)
- Code audit and more testing for my Bayesian logistic regression code.
How does one have confidence that code is correct? Is this more difficult
for code that produces random output having unknown properties than for other
computer code?
- Implement Bayesian model comparison for categorical data analysis
(log-linear models). Or any other interesting problem for that matter.
(already taken by Xiaoyan Li).
- Some other programming project of your choice.
- Applications of MCMC.
- Complicated (hierarchical) Bayesian models.
- Spatial statistics.
- Markov (but non-Poisson) spatial point processes.
- Spatial lattice processes (Ising models, Potts models,
Bayesian image reconstruction) (already taken by Song Liu).
- Statistical genetics (already taken by Jun Sheng).
- Monte Carlo maximum likelihood and Monte Carlo EM (already taken by Qiaoyang Lu).
- Bayesian decision theory.
- Some other application of your choice.
- MCMC methodology.
- Regeneration in MCMC (already taken by Barb Bennie).
- Simulated tempering, parallel tempering, umbrella sampling
(already taken by Michael Peascoe).
- MCMC so-called diagnostics.
- Sampler smorgasbord (slice, independence, random walk, MALA, hit and run,
Gibbs)
- Kinda-sorta MCMC: Griddy gibbs, Langevin diffusion, others
- Theory.
- Variance estimation methods other than batch means
(already taken by Kejia Shan).
- Perfect sampling (already taken by Junhui Wang).
- The Markov chain CLT. Conditions under which the CLT holds.
- Irreducibility, Harris recurrence and the LLN (already taken by Fan Yang).
- Geometric ergodicity. Drift conditions.