Computational Statistics
(1) Stochastic simulation: Generation of random variables; Acceptance and rejection methods; (2) Numerical optimization: EM algorithm; Simulated annealing. (3) Approximate inference methods: Laplace approximation; Importance sampling; Sequential Monte Carlo method; Monte Carlo integration. (4) Monte Carlo method via Markov chains: Gibbs sampler; Metropolis algorithm and Metropolis Hastings; Convergence diagnostics. (5) Calculation of marginal distribution: MCMC with reversible jumps; Comparison of models.
Basic Information
Workload
60 hours
Requirements
Statistical Modeling
Mandatory:
- Gamerman, D., Lopes, H. F. Markov Chain Monte Carlo: Stochastic Simulation for Bayesian Inference, Second Edition. Chapman & Hall, 2006.
- Braun, W. J. and Murdoch, D. J. (2016). A First Course in Statistical Programming with R, 2nd Edition, Cambridge University Press.
- Del Moral, Pierre, and Spiridon Penev. Stochastic Processes: From Applications to Theory. CRC Press, 2017.
Complementary:
- Thisted, R (1988). Elements of Statistical Computing.
- Robert, C.P., Casella, G. Monte Carlo Statistical Methods. Springer, 2004.
- Givens, G. H., Hoeting, J. A. Computational Statistics (Wiley Series in Computational Statistics), 2012.
- Gelman, A., Carlin, J. B., Stern, H. S. and Rubin, D. B. (2004). Bayesian data analysis, Chapman and Hall / CRC.
- Lange, Kenneth. Numerical analysis for statisticians. Springer Science & Business Media, 2010.