Computational Numerical Statistics
Code
10810
Academic unit
Faculdade de Ciências e Tecnologia
Department
Departamento de Matemática
Credits
6.0
Teacher in charge
Marta Cristina Vieira Faias Mateus
Weekly hours
4
Total hours
56
Teaching language
Português
Objectives
To be able to understand and apply the following statistical methods which need intensive use of the computer: algorithms of type Newton-Raphson, Monte Carlo, resampling techniques (Bootstrap e Jackknife), sampling-resampling techniques and iterative simulation (Monte Carlo via Markov Chain, MCMC method).
Teach the students all the basics and the theory which supports the algorithms and techniques tought in the course. Give the students different practical examples that illustrate the potentialities of the algorithms and techniques and which may allow them to solve those problems by using the software R, so that the students may have the capability to use the computer on an intensive basis by using the adequate available libraries, acquiring the capability to adequatelt modifying them in case of necessity.
Prerequisites
Basic notions of Analysis and Linear Algebra and intermediate level notions of Probability and Statistics.
Subject matter
1. Pseudo-random number generation (discrete and continuous).
2. Newton-Raphson method.
3. Fisher scoring method (generalized linear models).
4. Variance reduction techniques.
5. Resampling techniques: Bootstrap and Jackknife.
6. Monte Carlo methods.
7. Sampling-resampling methods.
8. Monte Carlo via Markov Chain (MCMC) methods: the Gibbs Sampler and Metropolis Hastings algorithms.
9. Application of the methods in different contexts (logistic, Poisson, Gaussian, Gamma regression, time series, hierarchical models, etc.)
10. Utilization of the learned techniques and adaptation of the libraries to practical case studies.
11. Writing of reports where, using statistical techniques, a full analysis of some case studies is done and conclusions drawn.
Bibliography
1. Davison, A.C., Hinkley, D.V., Bootstrap Methods and their Application, Cambridge University Press, 1997.
2. Gamerman, D., Lopes, H.F., Stochastic Simulation for Bayesian Inference, Chapman & Hall/CRC, 2006.
3. Gentle, J.E., Random Number Generation and Monte Carlo Methods, Springer-Verlag, 1998
4. Hossack, I.B., Pollard, J.H., Zehnwirth, B., Introductory Statistics with Applications in General Insurance, Cambridge University Press, 2nd Edition, 1999.
5. McCullagh, P., Nelder, J.A., Generalized Linear Models, London: Chapman and Hall, 1983.
6. Ross, S.M., Simulation, 3rd Edition, Academic Press, 2002.
7. Venables, W.N., Ripley, B.D., Modern Applied Statistics with S-Plus, Springer, 1996.
Teaching method
Classes/Labs where first the theoretical results are exposed, and secondly they are applied in the resolution of practical problems, proposed by the teacher. These problems are solved in a lab using the software R and the students are supposed to take part in their resolution.
Evaluation method
The evaluation of the course consists in four practical problems using the software R and with a written report, each work weights 25% . These problems can be solved in a group of two people at most and their resolution should be discussed with the teacher.