Advanced Statistical Models in Science and Engineering

Code:

M4015

Acronym:

M4015

Keywords
Classification	Keyword
OFICIAL	Mathematics

Instance: 2020/2021 - 2S

Active?	Yes
Responsible unit:	Department of Mathematics
Course/CS Responsible:	Master in Mathematical Engineering

Cycles of Study/Courses

Acronym	No. of Students	Study Plan	Curricular Years	Credits UCN	Credits ECTS	Contact hours	Total Time
M:ENM	8	Official Study Plan since 2013-2014	1	-	6	56	162
			2

Teaching language

Portuguese

Objectives

1. To provide the students with advanced regression techniques, including analyses of repeated measurements and analysis of longitudinal data, for continuous and discrete responses, and analyses of survival data
2. Implement statistical analyses in suitable software
3. Promote critical thinking in a data analysis process (data collection, modeling, interpretation of results, ...)

Learning outcomes and competences

1.Identification of scenarios of repeated measurements, longitudinal data or survival analysis
2. Identification of the most adequate model to the context of a given problem, among the studies models
3. Application and implementation of the studied models in R
4. Adequate interpretation of the results
5. Promotion of a critical thinking along the whole modelling process

Working method

Presencial

Pre-requirements (prior knowledge) and co-requirements (common knowledge)

Previous knowledge on multiple linear regression and logistic regression.

Program

1. (Gaussian) Linear mixed models

2. Generalized Linear Mixed Models

3. Survival Analysis

For all above mentioned models, the processes of estimation, inference, modelling and interpretation of results will be carefully studied.

Mandatory literature

José Pinheiro e Douglas Bates; Mixed Effects Models in S and S Plus , Springer, 2000. ISBN: ISBN-13: 978-1475781441
Molenberghs, G. and Verbeke, G.; Models for Discrete Longitudinal Data, Spinger, New York, 2005

Complementary Bibliography

Zuur Alain F., ed. lit. 340; Mixed effects models and extensions in ecology with R. ISBN: 978-1-4419-2764-4
Garrett M. Fitzmaurice; Applied longitudinal analysis. ISBN: 978-0-470-38027-7
Cabral M.S. & Gonçalves M.H. ; Análise de Dados Longitudinais, Sociedade Portuguesa de Estatística, 2011
Verbeke G. & Molenberghs G. ; Linear Mixed Models for Longitudinal Data, Spinger, New York, 2000

Teaching methods and learning activities

The classes have both a theoretical and a practical approach; the theory will be described and practical examples of application, in R, will also be presented.

Software

R

keywords

Physical sciences > Mathematics > Statistics

Evaluation Type

Distributed evaluation with final exam

Assessment Components

designation	Weight (%)
Trabalho escrito	67,00
Exame	33,00
Total:	100,00

Amount of time allocated to each course unit

designation	Time (hours)
Estudo autónomo	86,00
Frequência das aulas	56,00
Trabalho escrito	20,00
Total:	162,00

Eligibility for exams

Attendance is not mandatory.

Calculation formula of final grade

Students have to perform two individual written reports, with an oral presentation for each of them, and a final exam.The final mark will be the mean of the marks obtained in those three evaluation components. 
For final approval, students have to score more than 6 values (out of 20) on each of those three evaluation components.

Classification improvement

The mark obtained in the assignements cannot be improved; only the mark from the final exam.

Observations

1) Jury: Rita Gaio and Óscar Felgueiras.

2) The way the course will be provided is conditioned to the limitations imposed by FCUP according to the evolution of the pandemic COVID19. It is not expected a 100% face-to-face scheme.