Course detail

LCE5715 - Computational methods for inference with applications in R


Credit hours

In-class work
per week
Practice
per week
Credits
Duration
Total
3
1
8
15 weeks
120 hours

Instructor
Cristian Marcelo Villegas Lobos
Paulo Justiniano Ribeiro Junior
Roseli Aparecida Leandro

Objective
Present and discuss the main computational methods used in statistical inference. Provide computational complement to disciplines of the program. Empower participants to develop algorithms and write codes with views the implementations of models and extensions not contemplated in software implementations.

Content
Programming of the likelihood function for discrete variables, continuous or mixtures.
• programming of the Newton Raphson Algorithm
• programming of the Scoring of Fisher algorithm
• programming of the EM algorithm
• programming of the Gauss-Newton algorithm
• Methods of approximation of integrals Monte Carlo, Boostraping
• Exploration of the likelihood ratio, numerical likelihooh, profile likelihood and marginal likelihood.
• Methods for random effects models
• MCMC - Monte Carlo Markov chain

Bibliography
Albert, J. (2009) Bayesian Computation with R. Second Edition. New York: Springer.
Braun, W. J. ; Murdoch, D. J. (2007). A First Course in Statistical Programming with R. Cambridge University Press.
Gamerman, D. ; Lopes, H. F. (2006). Markov Chain Monte Carlo: Stochastic Simulation for Bayesian Inference. Second Edition. London: Chapman & Hall/CRC Press.
McLachlan, G. ; Krishnan, T. (1996). The EM Algorithm and Extensions. John Wiley & Sons, New York.
Ribeiro Jr, P. J., Bonat, W. H., Krainski, E. T. ; Zeviani, W. M. (2012). Métodos computacionais para inferência estatística. SINAPE.
Rizzo, M. (2008). Statistical Computing with R. CRC/Chapman Hall.
Robert, C. ; Casella, G. (2010). Introducing Monte Carlo Methods with R. New York: Springer.
Robert, C. ; Casella, G. (2004). Monte Carlo Statistical Methods (2a edição). Springer.
Tanner, M. A. (1996). Tools for statistical inference methods for the exploration of posterior distributions and likelihood functions. Springer, New York.
Venables, W. N. ; Ripley, B. D. (2002) Modern Applied Statistics with S. Fourth Edition. New York: Springer-Verlag.