Code |
14569
|
Year |
1
|
Semester |
S1
|
ECTS Credits |
6
|
Workload |
OT(15H)
|
Scientific area |
Mathematics
|
Entry requirements |
No prerequisites.
|
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.
|
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.
|
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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Language |
Portuguese. Tutorial support is available in English.
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