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# Statistical Inference

 Code: M4111 Acronym: M4111 Level: 400

Keywords
Classification Keyword
OFICIAL Mathematics

## Instance: 2020/2021 - 1S

 Active? Yes Responsible unit: Department of Mathematics Course/CS Responsible: Master's degree in Data Science

### Cycles of Study/Courses

Acronym No. of Students Study Plan Curricular Years Credits UCN Credits ECTS Contact hours Total Time
M:DS 6 Official Study Plan since 2018_M:DS 1 - 6 42 162

### Teaching Staff - Responsibilities

Teacher Responsibility
Laura Luciana Cavalcante de Sousa

### Teaching - Hours

 Theoretical and practical : 3,00
Type Teacher Classes Hour
Theoretical and practical Totals 1 3,00
Laura Luciana Cavalcante de Sousa 0,00

### Teaching language

Suitable for English-speaking students

### Objectives

Acquire a solid knowledge in inductive statistics and develop capacities and skills in statistical modelling techniques, fundamental to the presentation, analysis and interpretation of data sets.

### Learning outcomes and competences

Upon completing this course, the student should:

- have a deep understanding of the fundamental concepts and principles of statistics;

- know the fundamental parametric and nonparametric statistical methods, how to apply them to concrete situations and be able to interpret and communicate the obtained results;

- be able to use the programming language R to analyze different types of data and solve statistical problems.

Presencial

### Program

Basic concepts of probability theory and some probabilistic models (structured review during the course).

Statistical models. Exponential families. Data reduction: Sufficiency and completeness.

Point and intervalar estimation. Maximum likelihood principle. Derivation and comparison of estimators. Minimum variance unbiased estimation and efficiency. Large sample theory, Confidence regions.

Simulation based inference. Resampling methods. Randomization tests.

Nonparametric inference. Order statistics and the vector of ranks. Goodness of fit tests. Rank-based tests. Measures and tests of association for two variables.

Parametric hypotheses testing. Optimality criteria. Likelihood ratio tests.

### Mandatory literature

Casella George; Statistical inference. ISBN: 0-534-24312-6
Nolan Deborah; Stat labs. ISBN: 0-387-98974-9
Rice John A. 1944-; Mathematical statistics and data analysis. ISBN: 9780495118688

### Teaching methods and learning activities

Lectures TP where the topics of the syllabus are presented, exercises and related problems form the Problem Sheets are solved and discussed. The concepts and methods are illustrated and motivated by examples of different kinds. Both the theoretical developments of the methods and their application in practice are considered, using whenever appropriate, the statistical software R.

Project work to be developed in team. The discussion of the works is open, all students are encouraged to participate.

All resources are available for students at the unit’s web page.

R project

### Evaluation Type

Distributed evaluation with final exam

### Assessment Components

designation Weight (%)
Exame 60,00
Trabalho prático ou de projeto 40,00
Total: 100,00

### Amount of time allocated to each course unit

designation Time (hours)
Estudo autónomo 96,00
Frequência das aulas 56,00
Trabalho escrito 10,00
Total: 162,00

### Eligibility for exams

Practical assignments/ Project submitted within the fixed  schedules.

### Calculation formula of final grade

The evaluation comprehends two components: project (40%) and final exam (60%). A minimum rating of 30% is required in each of the evaluation components.

### Classification improvement

The classification obtained in the project component is not subject to improvement and is only valid during the current academic year.

### Observations

Juri: Margarida Brito and Rita Gaio