Master Program in Data Science and Engineering

Master Program in Applied Mathematics and Computation

(Instituto Superior Técnico - Universidade de Lisboa)


SYLLABUS

  1. Introduction: revision of classical methods of statistical inference, summary of Bayesian inference, use of stochastic simulation ([G]: Chap.1,7; [R]: Chap.1,2,3; [T]: Chap.1,2; [P]: Chap.1,2,3).

  2. Classic methods of estimation and algorithms: maximum likelihood, Newton-Raphson, EM, data augmentation ([G]: Chap.6,15,17; [R]: Chap.11; [P]: Sec.9.3.2).

  3. Traditional Monte Carlo methods: generation of pseudo-random numbers, simple Monte Carlo, Monte Carlo with importance sampling ([G]: Chap.11; [R]: Chap.5,6; [T]: Chap.4; [P]: Chap.7).

  4. Monte Carlo Markov chain methods: Gibbs sampler, Metropolis-Hastings algorithm, convergence diagnostic techniques ([G]: Chap.7,11; [R]: Chap.9; [T]: Chap.6; [P]: Chap.9,10).

  5. Statistical models: model assessment, applications to various statistical problems ([G]: Chap.9,17; [T]: Chap.3,5; [P]: Chap.4,6,8,11).

  6. Resampling methods: bootstrap, jackknife ([G]: Chap.12,13; [R]: Chap.7).


BIBLIOGRAPHY

  1. Recommended bibliography:
  2. Optional bibliography:
    • Paulino, C.D., Amaral Turkman, A., Murteira, B., Silva, G.L. (2018). Estatística Bayesiana, 2a edição. Fundação Calouste Gulbenkian, Lisboa. ([P])
    • Morettin, P.A., Singer, J.M. (2025). Estatística e Ciências de Dados, 2a edição. LTC, São Paulo.
    • Härdle, W., Okhrin, O., Okhrin, Y. (2017). Basic Elements of Computational Statistics. Springer.
    • Hastie, T., Tibshirani, R., Friedman, J. (2009). The Elements of Statistical Learning. Data Mining, Inference, and Prediction, 2nd edition. Springer-Verlag.
    • Gamerman, D., Lopes, H.F. (2006). Markov Chain Monte Carlo: Stochastic Simulation for Bayesian Inference, 2nd edition. Chapman & Hall/CRC, London.
    • Marin, J.-M., Robert, C.P. (2007). Bayesian Core - A Practical Approach to Computational Bayesian Statistics. Springer, New York.
    • Tanner, M.A. (1996). Tools for Statistical Inference, 3rd edition. Springer-Verlag, New York.
    • Wickham, H., Grolemund, G. (2017). R for Data Science: Import, Tidy, Transform, Visualize, and Model Data. O’Reilly Media.
    • Ross, S.M. (2020). Introduction to Probability and Statistics for Engineers and Scientists, 6th edition, Academic Press. (preliminary basic reference: Chap.1-9)
    • Silva, G.L. (2024). Notas de Probabilidades e Estatística, 3a edição. Lisbon: Instituto Superior Técnico. (preliminary basic reference)


STATISTICAL SOFTWARE

R (http://www.r-project.org/ + RStudio), SAS, SPSS, STATA, JAGS, Stan, OpenBugs, INLA.


EVALUATION METHODOLOGY

The final grade is a weighted average of the (two-student-group) practical report grade (30%) and the test or exam grade (70%). The test grade is the simple average marks of the grades of two 45-minute tests and there is only one 2-hour exam. Report grade is subject to the possibility of discussion, while the final grade of at least 17.5 marks to the oral exam.


OBJECTIVES

To understand and be able to apply statistical methods in computationally intensive contexts, paying special attention to issues of representative sampling extraction and generation and statistical inferences associated with various types of data sets.


INFORMATION