# Computational Numerical Statistics

## 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.

## General characterization

10810

6.0

##### Responsible teacher

Vanda Marisa da Rosa Milheiro Lourenço

Weekly - 4

Total - 56

Português

### Prerequisites

 Basic notions of Analysis and Linear Algebra and intermediate level notions of Probability and Statistics. Some basic programming notions.

### 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

1 - ATTENDANCE
In order to be evaluated in this course, the student must obtain course attendance or be exempted from it.
In order to obtain course attendance, the student is required to simultaneously verify the following two prerequisites:
(i) the student did not unjustifiably miss more than 4 theoretical-practical classes, or the student benefits of a special status that exempts he/she from class attendance;
and
(ii) the student carried out at least two of the three group projects, specifically, either the 1st with the 3rd group projects or the 2nd with the 3rd group projects, as the 3rd group project has an associated minimum grade for final approval.
A particular student, that while fulfilling the two points above did not pass the course, is exempted from ENC classes in the following academic year, should he/she enroll again in the course. Nonetheless, the student will still be required to again carry out all the group project evaluations.
When obtained, attendance is only valid through the next academic year.

2 – KNOWLEDGE EVALUATION
The type of evaluation of the courseis continuous evaluation via a project component.
2.1 – Continuous assessment
Continuous evaluation for this course consists of three group projects, valued for 8, 8 and 4 points, respectively. The third and last group project has a minimum pass grade of 1.5 points without which the student will fail the course.
The group projects will involve both theory and hands-on computational problems that need to be solved using the software R. The grading of those also presumes a possible discussion with the Professor. The gradings of the students may differ withing groups. It is intended a group membership rotation from project to project.
A student passes the course if the sum of the points referring to the three group projects is greater or equal than 9.5 points and as long as the grading of the third group project is greater or equal than 1.5 points, as already mentioned above.
2.2 – Supplementary Exam
There is no supplementary exam in this course.
2.3 – Supplementary season
A student that having obtained course attendance did not pass the course, can still have a chance of passing the course by carrying out one or more, now individual, theoretical-computational projects until the end of the supplementary exam season.
Please see point 4 of the article 8º of the Regulamento de Avaliação de Conhecimentos da FCT-UNL.

## Subject matter

1. Generation of random variables (discrete and continuous).
2. Method of Newton-Raphson.
3. Method of Fisher scoring (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.

## Programs

Programs where the course is taught: