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Computational Numerical Statistics

Objectives

To discuss the theory behind the algorithms and techniques taught in the course, while illustrating the use of those in several statistical contexts via the R software. Provide the students with the ability of making intensive use of the computer in statistical problem solving, resorting both to R functions and packages as well as to direct programming of the methods in the R language.

General characterization

Code

10810

Credits

6.0

Responsible teacher

Regina Maria Baltazar Bispo

Hours

Weekly - 4

Total - 52

Teaching language

Português

Prerequisites

Basic notions of Analysis (mostly integral calculus) and Linear Algebra (mostly matrix algebra)  and intermediate level notions of Probability and Statistics. Basic programming skills.

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

Each class will have an associated theoretical and practical component. It is intended that students are first acquainted with the statistical theory and its related computational issues and then given some hands-on problems to solve using the R software.

It is expected that all students engage in the practical activities.

Evaluation method

It includes 3 group projects (P1, P2 and P3), covering theory and hands-on computational problems that should be solved using R, with a weight of 35%, 35% and 30%, respectively.

Subject matter

Succintly,

1. Generation of random variables: methods of the inverse transform and acceptance-rejection

2. Optimization: methods of bissection, Newton-Raphson and Fisher scoring

3. Monte Carlo methods: estimation and variance reduction techniques

4. Resampling techniques: methods of Bootstrap and Jackknife

5. Bayesian inference and computation: Monte Carlo (MC) and Monte Carlo via Markov Chain (MCMC) methods

Transversely the syllabus of this course includes:

6. Application of the studied methods in several contexts (e.g., linear regression, generalized linear models, etc.)

7. Knowledge of the R built-in functions and packages that refer to the statistical computational techniques learned and the applications that were presented

8. Report writing with full documentation and theoretical scientific ground of the statistical analysis and conclusions drawn in the computational project assignments