# 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

Vanda Marisa da Rosa Milheiro Lourenço

##### Hours

Weekly - 4

Total - 56

##### 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

**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 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;

and

(ii) the student satisfactory carried out the homework assignments (grading >= 1.25).

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 and should class attendance be mandatory. Nonetheless, the student will still be required to again carry out all the group project and other evaluations.

When obtained, attendance is only valid through the next academic year.

One notes that, exceptionally, and because ENC classes are exclusively online, this semester ENC class attendance is not mandatory.

**2 – KNOWLEDGE EVALUATION**

The type of evaluation of the course is continuous evaluation via a project component.

2.1 – Continuous assessment

Continuous evaluation for this course consists of three group projects, valued for 7, 7 and 3.5 points, respectively, in addition to individual homework assignments valued for 2.5 points.

The third and last group project has a minimum pass grade of 1.0 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.

A student passes the course if the sum of the points referring to the three group projects and the homework assignments is greater or equal than 9.5 points and as long as the grade of the third group project is greater or equal than 1.0 points, as already mentioned above.

2.2 – Supplementary Exam

There is no supplementary exam in this course.

2.3 – Supplementary evaluation 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 up to two*, now individual, theoretical-computational projects until the end of the supplementary evaluation season.

* This point assumes that a student can only redo up to two projects, which will necessarily have to be the 1st with the 3rd or the 2nd with the 3rd. It will not be possible for a student to redo the 3 projects nor the 1st and 2nd together in order to pass the course. Due to these particulars, this process needs to be carefully addressed and decided between both the student and the Professor in early January.

**3 – COURSE GRADE IMPROVEMENT**

Please see point 4 of the article 8º of the Regulamento de Avaliação de Conhecimentos da FCT-UNL.

## 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

## Programs

Programs where the course is taught: