Topics in Computational Statistics
Sustainable Development Goals
Learning Goals
Acquisition of knowledge in the area of Computational Statistics with the use of the R Software. Simulation approach and the computational methods commonly used in statistics. Topics of classical statistical computing in optimization, integration and applications to Statistical Inference Methods Monte Carlo (MC), MC integration, simulation methods and Markov Chain Monte Carlo (MCMC), the EM algorithm and others.
To familiarize the students with the computational treatment of data.
To develop simulation algorithms and computational techniques used in statistics.
To know the main foundations relating to the environment R.
To dominate techniques of parametric and nonparametric statistical inference.
To generate pseudo-random numbers and random variables for simulation methods.
To understand and be able to apply the method of bootstrap resampling.
To recognize and to know how and when to apply nonparametric approaches.
To stimulate autonomous learning and adaptation to new situations.
Contents
1. Introduction to the R language.
2. Generation of Pseudo-Random Numbers.
3. Monte Carlo Methods in Statistical Inference.
4. Resampling methods: Bootstrap, Jackknife.
5. Markov Chain Monte Carlo methods (MCMC).
6. ML estimation and the EM algorithm.
Teaching Methods
Theoretical-practical lessons mainly lectured with a blackboard, with e-learning tools, and transparencies.
Motivation of student’s attendance to the classroom and student’s continuous work.
Computational applications accomplishment.
Introduction to theoretical concepts appealing to different areas of applications to illustrate the importance of course contents. Exercises with emphasis in the resolution of real problems, to motivate interest in the course and to demonstrate its utility.
To stimulate individual and group participation within the classroom and at home.
To emphasize the critical analysis and interpretation of data, appealing to software outputs as much as possible.
Assessment
Evaluation: To privilege continued evaluation carrying out one test plus individual/group homework projects. If continuous evaluation is not feasible for the student, a final examination is possible, but the individual / group project is still required although with lesser weight for final grade.
Recommended Reading
1. Efron, B.; Tibshirani, R. F. An Introduction to the Bootstrap. Chapman & Hall.
2. Gentle, J. E (2002). Elements of Computational Statistics, Springer.
3. Gentle, J. E.; Hardle, W.; Mori, Y. (2004): Handbook of Computacional Statistics: Concepts and Methods, Springer.
4. Rizzo, M. L. (2008). Statistical Computing with R, Chapman and Hall CRC.
5. Robert, C. P., Casella, G. (2010). Introducing Monte Carlo Methods with R, Springer-Verlag, New Work.
6. Rubinstein, R. Y.; Kroese, D. P. (2007). Simulation and the Monte Carlo Method. Toronto-Canadá: John Wiley.
