# Estatística Numérica Computacional

## Objectives

Students should 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). Students should be able to use the statistic software R in applied problems, by using the adequate available libraries or by adequately modifying them in case of necessity. Students should further be able to write reports where, using statistical techniques, a full analysis of the study case is done and well justified conclusions are drawn.

## General characterization

##### Code

12023

##### Credits

4.0

##### Responsible teacher

Isabel Cristina Maciel Natário

##### Hours

Weekly - 3

Total - 41

##### Teaching language

Português

### Prerequisites

Basic notions of Analysis and intermediate level notions of Probability and Statistics.

### Bibliography

Albert J., Bayesian Computation with R, Springer, 2007.

Crawley, M. J., The R Book, 2nd Edition, Wiley, 2012.

Davison, A.C., Hinkley, D.V., Bootstrap Methods and their Application, Cambridge University Press, 1997.

Gamerman, D., Lopes, H.F., Stochastic Simulation for Bayesian Inference, Chapman & Hall/CRC, 2006.

Gentle, J.E., Random Number Generation and Monte Carlo Methods, Springer-Verlag, 1998.

Gentle, J.E., Computacional Statistics, Springer, 2009.

Hossack, I.B., Pollard, J.H., Zehnwirth, B., Introductory Statistics with Applications in General Insurance, Cambridge University Press, 2nd Edition, 1999.

Rizzo, M.L., Statistical Computing with R. Chapman & Hall/CRC, 2007.

Robert, C., Casella, G., Introducing Monte Carlo Methods with R, Springer, 2010.

Ross, S.M., Simulation, 3rd Edition, Academic Press, 2002.

### Teaching method

The curricular unit is divided into 4 learning units that include each 2-3 videos of oral exposition of the contents, of 10-15 minutes each, along with the presentation of examples and complemented by solved proposed exercises. In the end of each learning unit a revising exercise is delivered. During the learning units presentation two evaluation assignments are distributed, contributing for the final grading. A timetable for explaining doubts to students made is available via Skype.

### Evaluation method

Two theoretical-practical assignments, needing R programming, one for each 2 curricular units (50% + 50%).

## Subject matter

1. Pseudo-random number generation (discrete and continuous).

2. Newton-Raphson method.

3. Variance reduction techniques.

4. Resampling techniques: Bootstrap and Jackknife.

5. Monte Carlo methods.

6. Numerical optimization for the maximum likelihood method.

7. Fisher scoring method.

8. Sampling-resampling methods.

9. Monte Carlo via Markov Chain (MCMC) methods: the Gibbs Sampler and Metropolis Hastings algorithms.

10. Use of the taught 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.