Checking date: 03/07/2020

Course: 2020/2021

Statistical Modeling
(15449)
Study: Master in Mathematical Engineering (70)
EPI

Coordinating teacher: DURBAN REGUERA, MARIA LUZ

Department assigned to the subject: Department of Statistics

Type: Compulsory
ECTS Credits: 6.0 ECTS

Course:
Semester:

Students are expected to have completed
Competences and skills that will be acquired and learning results.
-Use linear and smooth regresseion models as a tool to quantify the relationship between variables. -Perform statistican inference on the parameters of the models -Know the assumptions behind each model and the consequences of this assumptions not being satisfied.
Description of contents: programme
1. Introduction: Multivariate regression 1.1 Matrix representation of the model 1.2 Parameter estimation 1.3 Residuals 1.4 Inference 1.5 Multicolinearity 2. Generalized least squares 2.1 Weighted least squares 2.2 Iterative Reweighted least squares 3. Introduction to generalized linear models 3.1 The exponential family of distributions 3.2 Components of a GLM 3.3 Estimation: Fisher Scoring Algorithm 3.4 Inference 3.5 Diagnostics in GLMs 4. Models for Binomial/Binary data 4.1 Link functions 4.2 Estimation and parameter interpretation 4.3 Infernce 4.4 Validation of the model: ROC curve 4.5 Diagnostics 5. Other glm models 5.1 Multinomial regression 5.2 Models for ordinal data 5.3 Poisson regression 6. Smoothing methods 6.1 Pollynomial regression 6.2 Kernels 6.3 Splines 6.4 Generalized additive models with P-splines 6.5 P-splines: basis and penalties 6.6 Parameter estimation and degrees of freedom 6.7 Smoothing parameter selection 6.8 P-splines as mixed models
Assessment System
• % end-of-term-examination 60
• % of continuous assessment (assigments, laboratory, practicals...) 40
Basic Bibliography
• Dobson, A. An introduction to generalized linear models. Chapman and Hall.
• Hastie, T. y Tibshirany, R.. Generalized additive models. Chapman and Hall.
• McCullagh, P. y Nelder, J.. Generalized linear models. Chapman and Hall.
• Myers, R.H. and Montgomery,D.C.. Generalized Linear Models: With Applications in Engineering and Sciences. Wiley.
• Wood, S.. Generalized Additive Models: An Introduction with R . Chapman and Hall.

The course syllabus and the academic weekly planning may change due academic events or other reasons.