# Statistical Modeling and Inference

## Objectives

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

10818

6.0

##### Responsible teacher

Manuel Leote Tavares Inglês Esquível

Weekly - 4

Total - 56

Português

### Prerequisites

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.

### Bibliography

• 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 70% 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

Programs where the course is taught: