Computational Statistics

Basic information

Workload: 

45 hours

Prerequisite: 

Mathematical Statistics 

Syllabus: 

Stochastic simulation: Generation of random variables; Acceptance and rejection methods. Numerical optimization: EM algorithm; Simulated annealing. Approximate inference methods: Laplace approximation; Importance sampling; Monte Carlo Integration, Sequential Monte Carlo Methods. Monte Carlo method via Markov Chains: Gibbs sampler; Metropolis and Metropolis Hastings algorithm; Convergence diagnostics. Calculation of marginal distribution: reversible jump MCMC; Comparison of models.

 

Bibliography

Mandatory: 

·   Gamerman, D., & Lopes, H. F. (2006). Markov chain Monte Carlo: stochastic simulation for Bayesian inference. Chapman and Hall/CRC.
·    Robert, C. P., Casella, G. (2004). Monte carlo methods. John Wiley & Sons, Ltd.
·    Del Moral, P., & Penev, S. (2017). Stochastic Processes: From Applications to Theory. CRC Press.

Complementary: 

·       Givens, G. H., & Hoeting, J. A. (2012). Computational statistics (Vol. 710). John Wiley & Sons.
·       Wang, X., Ryan, Y. Y., & Faraway, J. J. (2018). Bayesian Regression Modeling with INLA. CRC Press.
·       Gentle, J. E., Härdle, W. K., & Mori, Y. (Eds.). (2012). Handbook of computational statistics: concepts and methods. Springer Science & Business Media.
·       Liu, J. S. (2008). Monte Carlo strategies in scientific computing. Springer Science & Business Media.
·       Efron, Bradley, and Trevor Hastie. Computer age statistical inference. Vol. 5. Cambridge University Press, 2016.