| Code |
14808
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| Year |
3
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| Semester |
S1
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| ECTS Credits |
6
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| Workload |
TP(60H)
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| Scientific area |
Mathematics
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Entry requirements |
NA
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Learning outcomes |
It is intended that students use statistical methods that require an intensive use of the computer, related to random number generation, simulation of probability distributions, simulation of p-values of the hypothesis tests, re-sampling, Monte Carlo methods, MCMC methods, etc.
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Syllabus |
1. Introduction to R.
2. Random numbers generation: Pseudo-random numbers; Methods for generating random variables (inverse-transform method; acceptance-rejection method; transformations).
3. Monte Carlo Methods: Simulation and Monte Carlo integration; Variance reduction; Importance sampling; Stratified sampling; Applications to statistical inference.
4. Likellihood: Maximum likelihood method; Score function; Fisher’s information; Expectation-maximization (EM) algorithm.
5. Resampling methods: Bootstrapping; Jackknife resampling; Cross validation.
6. Markov chain Monte Carlo methods (MCMC): Markov Chains (discrete-time Markov chains; birth-death process); The Hastings-Metropolis Algorithm; Gibbs sampler; Convergence of MCMC methods
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Main Bibliography |
S. Ross.” Simulation”, Fourth Edition. Academic Press, 2006.
S. Ross. “Introduction to Probability and Statistics for Engineers and Scientists”. John Wiley & Sons, 1987.
J. Kleijnen. “Statistical Techniques in Simulation”, Volumes I, II. Marcel Dekker, Inc., 1974.
B. Efron and R. F. Tibshirani. “An Introduction to the Bootstrap”. Chapman & Hall, 1993.
M. R. Chernick, “An introduction to bootstrap methods with applications to R”. John Wiley & Sons, 2011.
G. H. Givens and J. A. Hoeting. “Computational Statistics”, Second Edition. John Wiley & Sons, 2013.
M. L. Rizzo. “Statistical Computing with R”. Chapman & Hall/CRC, 2008.
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Language |
Portuguese. Tutorial support is available in English.
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