Computational Numerical Statistics

General characterization

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

The classes for this course encompass both theoretical and practical aspects. The aim is to begin with a theoretical presentation of the statistical methods to be covered and their computational specifics, followed by solving problems proposed by the professor using the R software.

Students are expected to engage and participate actively in solving the presented problems.

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 attended more than 2/3 of the classes.

A student who fulfills the two points above but does not pass the course is exempt from ENC classes in the following academic year, should they enroll in the course again and if class attendance is mandatory. Nonetheless, the student will still be required to complete all group projects and other evaluations again.

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

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 7.5, 7.5 and 5 points, respectively. The third and last group project has a minimum pass grade of 2 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 with course attendance 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 grade of the third group project is greater or equal than 2 points, as already mentioned above.

2.2 – Resit Exam

There is no resit exam in this course.

2.3 – Resit period

A student who, despite having attended the course, did not pass can still have a chance to pass by completing or repeating one individual theoretical-computational project by the end of the supplementary evaluation period.

• This point assumes that a student can redo or repeat (not the same handout, obviously) one of the projects by the end of the supplementary evaluation period. If the student did not achieve the minimum grade on Project 3, then this is the project that must be repeated.

Due to these specifics, this process needs to be carefully discussed and decided between 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: