Course detail

LCE5715 - Computational Methods for Inference with Applications in R

Credit hours

In-class work
per week
per week
15 weeks
120 hours

Cristian Marcelo Villegas Lobos
Marcelo Andrade da Silva

Present and discuss the main computational methods used in statistical inference, provide a computational complement to the program's disciplines, and enable students to develop algorithms and write codes with a view to implementing statistical models and extensions.

Study of computational methods with programming algorithms aimed at statistical inference.
1. Likelihood function.
2. Numerical estimation methods.
2.1 Newton-Raphson method.
2.2 Fisher Scoring Algorithm.
2.3 EM Algorithm.
3. Numerical integration methods.
3.1 Gaussian quadrature.
3.2 Laplace approximation.
3.3 Monte Carlo Integration.
4. MCMC Simulation.
4.1 Metropolis-Hastings.
4.2 Gibbs sampler.
5. Simulation studies in statistical models.
6. Resampling methods.
6.1 Jackknife method.
6.2 Bootstrap method.

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.
EFRON, B. The Jackknife, the Bootstrap, and other resampling plans. California: Stanford Univeristy, 1980.
Gamerman, D. ; Lopes, H. F. (2006). Markov Chain Monte Carlo: Stochastic Simulation for Bayesian Inference. Second Edition. London: Chapman & Hall/CRC Press.
Gelman, A; Carlin, J.; Stern, H; Dunson, D. Vehtari, A; Rubin, D. (2015). London: Chapman & Hall/CRC Press. Third Edition.
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.