| Code |
14569
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| Year |
1
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| Semester |
S1
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| ECTS Credits |
6
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| Workload |
OT(15H)
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| Scientific area |
Mathematics
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Entry requirements |
No prerequisites.
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Learning outcomes |
It is intended that students use statistical methods that require an intensive use of 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. Random numbers.
2. Simulation of discrete and continuous random variables: The inverse transform method; Rejection method.
3. Goodness of fit tests: Chi-square test; Kolmogorov-Smirnov test and Lilliefors significance correction; Shapiro-Wilk test.
4. Numerical Methods for Maximum Likelihood Estimation: basics optimization; maximum likelihood estimation, expectation-maximization (EM).
5. Resampling: Cross validation; Jackknife; Bootstrap.
6. Markov chain Monte Carlo methods: Basic concepts of Markov chains; The Hastings-Metropolis Algorithm; Gibbs Algorithm.
7. Use of statistical software: R, SPSS, MATLAB, etc.
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Main Bibliography |
S. Ross.” Simulation”, Fourth Edition. Academic Press, 2006.
S. Ross. “Intoduction 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.
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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Teaching Methodologies and Assessment Criteria |
This course will only have a tutorial monitoring. Thus, students will be guided every week to enable them to archive different goals.
The final evaluation will consist of a project and its oral presentation.
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Language |
Portuguese. Tutorial support is available in English.
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