This class is the continuation of the Bayesian Topics (Stat 32300/HSTD 43000). We will move beyond the material learned there (the basics of Bayesian statistics and computation (importance sampling, EM, MCEM, data augmentation, Metropolis-Hastings and Gibbs sampling). In particular, we will focus on extensions to MCMC geared for dealing with high-dimensional problems with potential multimodality (simulated tempering, sequential Monte Carlo, Hamiltonian MCMC, Langevin MCMC). We will also discuss issues and algorithms for model comparison (transdimensional MCMC and algorithms for computating (ratios of) normalizing constants). Algorithms can be implemented in any language; familiarity with R or Matlab will be assumed. The class will have a seminar/discussion format, and focus on actual algorithm implementation. The students will be expected to complete a data analysis project by the end of the course. There will be a final in-class presentation.
Prerequisites: