Statistical Modeling and Inference


Develop skills in the analysis of complex concrete situations leading to the use of relevant statistical models.

Deepening of the fundamental concepts necessary for a complete exploration of statistical models.

General characterization





Responsible teacher

Manuel Leote Tavares Inglês Esquível


Weekly - 4

Total - 56

Teaching language



Ideally, the knowledge of Mathematical Analysis, Linear Algebra and programming in an advanced language - Python, C ++, Java - usually acquired in the first two years of a first degree in Mathematics.


  • A. Agresti. An Introduction to Categorical Data Analysis. Wiley Series in Probability and Statistics. Wiley, 2007.
  • J. Gill. Generalized Linear Models: A Unified Approach. Quantitative Applica-tions in the Social Sciences. SAGE Publications, 2000.
  • T. Hothorn and B.S. Everitt. A Handbook of Statistical Analyses Using R. CRC Press, 2006.
  • P. McCullagh and J.A. Nelder. Generalized Linear Models, Second Edition. Chapman & Hall/CRC Monographs on Statistics & Applied Probability. Taylor & Francis, 1989.
  • Randall Pruim. Foundations and Applications of Statistics: An Introduction Using R. Pure and Applied Undergraduate Texts. American Mathematical Society, 2011.
  • P. de Jong and G. Z. Heller. Generalized Models for Insurance Data. Cambridge University Press, 2008.

Teaching method

Participated theoretical and practical classes, with oral exposition and problem solving with laptops.

Evaluation method

The evaluation consists of two interim tests, a practical computational work and, if necessary, a final exam. The tests and work will give rise to a continuous evaluation grade (weighted average with 60% for the tests with the second weight 2 and the first weight 1). To obtain attendance the student must have attended at least two thirds of the classes and must have performed the tests and work.

Subject matter

1. Review of fundamental concepts of point estimation and interval estimation

2. The Exponential Family of Distributions

2.1. The Exponential Family of 1 and Multiple Parameters: Fundamental Concepts and Outcomes

2.2. Exponential Family Distributions

2.3. Exponential Family Estimation

3. Generalized Linear Models

3.1. Error Distributions as Exponential Family Members

3.2. The binding function - canonical linking function and non-canonical linking functions

3.3. The Linear Model as a Particular Case

3.4. Logit Templates

3.5 Log Linear Models

3.6. Random Effects Templates and Mixed Templates

4. Nonlinear Models


Programs where the course is taught: