Statistical Inference

Code:

M4143

Acronym:

M4143

Level:

400

Keywords
Classification	Keyword
OFICIAL	Mathematics

Instance: 2024/2025 - 1S

Active?	Yes
Responsible unit:	Department of Mathematics
Course/CS Responsible:	Master in Computational Statistics and Data Analysis

Cycles of Study/Courses

Acronym	No. of Students	Study Plan	Curricular Years	Credits UCN	Credits ECTS	Contact hours	Total Time
M:ECAD	33	Study plan since 2021/2022.	1	-	9	63	243

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.

 

Working method

Presencial

Program

Random variables and random vectors. Most common distributions. Characteristic functions. Stochastic convergence. Laws of large numbers and central limit theorem. General principles of the classical statistical inference.

Statistical models. Exponential families. Sufficiency. Maximum likelihood principle.

Derivation and comparison of estimators. Efficiency. Confidence regions.

Elements of Bayesian inference. Bayesian approach versus classical approach. A priori distribution and a posteriori distribution. Conjugate distributions. Bayes estimators.

Nonparametric inference. Goodness of fit tests. Rank-based tests. Measures and tests of association for two variables.

Parametric hypotheses testing. Optimality criteria.

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

Complementary Bibliography

Wasserman, Larry ; All of Nonparametric Statistics, Springer-Verlag New York, 206. ISBN: 978-0-387-25145-5 (DOI: 10.1007/0-387-30623-4)

Teaching methods and learning activities

Each lecture lasts for 2 hours. Whenever possible, the last half hour of each one will be spent with exercises/examples. Pertinent list of exercises will be provided to students.

The discussion of the works is open, all students are encouraged to participate.

All resources will be made available to the students.

Software

R project

Evaluation Type

Distributed evaluation with final exam

Assessment Components

designation	Weight (%)
Exame	40,00
Trabalho prático ou de projeto	45,00
Trabalho escrito	15,00
Total:	100,00

Amount of time allocated to each course unit

designation	Time (hours)
Estudo autónomo	160,00
Frequência das aulas	63,00
Trabalho escrito	5,00
Trabalho laboratorial	15,00
Total:	243,00

Eligibility for exams

Practical assignments/ Project submitted within the fixed  schedules.

Calculation formula of final grade

Distributed evaluation with final exam. Written exam ( E ) and laboratorial work/project (P). Final classification (E*8+P*12)/20. Minimum mark of E and P: 40%.

Classification improvement

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