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Statistics 8701 (Geyer) Spring 2002 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.
  • 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.
  • Some other programming project of your choice.
• Applications of MCMC.
  • Complicated Bayesian models.
  • Spatial statistics.
    • Markov (but non-Poisson) spatial point processes.
    • Spatial lattice processes (Ising models, Potts models, Bayesian image reconstruction).
  • Statistical genetics.
  • Monte Carlo maximum likelihood (like problem #2 on homework #4 but with MCMC instead of GOFMC).
  • Some other application of your choice.
• Theory.
  • Variance estimation methods other than batch means.
  • Perfect sampling.
  • The Markov chain CLT. Conditions under which the CLT holds.
  • Irreducibility, Harris recurrence and the LLN.
  • Geometric ergodicity. Drift conditions.