Statistical Modeling and Inference
Code
10818
Academic unit
Faculdade de Ciências e Tecnologia
Department
Departamento de Matemática
Credits
6.0
Teacher in charge
Carlos Manuel Agra Coelho
Weekly hours
4
Total hours
56
Teaching language
Português
Objectives
We want the student to obtain a solid knowledge in areas of inference and statistical modelization which, usually, are not taught at the undergraduate level. Emphasis is placed in aspects related with statistical modelization presented in a more general context than just only the linear model setting, in such a way that the student may acquire a wider view of the modelization and inference process, which is essential for everyone that is willing to make solid applications in their future professional life. The association between modelization and inference wants to give this more embracing view and the possibility of applications in several areas, since Generalized and Mixed linear models, taught in this course, allow for a wide range of applications of statistical inference in many areas.
Prerequisites
Basic notions of Analysis and Linear Algebra and intermediate level notions of Probability and Statistics and -Estimation.
Subject matter
- Review of fundamental concepts about point and interval estimation
- The Exponential family of distributions
- The Exponential family of 1 and several parameters: fundamental concepts and results
- Distributions in the Exponential family
- Estimation in the Exponential family
- Generalized Linear Models
- Error distributions as members of the Exponential family
- The link function - canonical and non-canonical link functions
- The Linear Model as a particualr case
- Logit models
- Log-linear models
- Random effects and Mixed effects models
- Non-linear models
Bibliography
McCullagh, P., Nelder, J. A. (1989). Generalized Linear Models, 2ª ed. Chapman & Hall/CRC, New York.
Gill, J. (2000). Generalized Linear Models: a Unified Approach. SAGE University Papers 134, 122pp.
Khuri, A. I., Mathew, B., Sinha, B. K. (1998). Statistical Tests for Mixed Linear Models. J. Wiley & Sons, New York.
Agresti, A. (1996). An Introduction to Categorical Data Analysis. J. Wiley & Sons, New York.
Coelho, C. A. (2007). Tópicos em Probabilidades e Estatística – Vol III, Cap. 7, 10, 11.
Teaching method
Classes/Labs where, after the exposition of the theoretical results and bases concerning each topic, the students are supposed to take part in the resolution of practical problems.
Evaluation method
The evauation of the course will be done through the realization of 2 midterms, with a wieght of 30% each for the final grade, and the resolution of 2 sets of problems, each one of them with a weight of 20% for the final grade.