2025
Statistical Inference
Name: Statistical Inference
Code: MAT13618M
6 ECTS
Duration: 15 weeks/156 hours
Scientific Area:
Mathematics
Teaching languages: Portuguese
Languages of tutoring support: Portuguese
Regime de Frequência: Presencial
Sustainable Development Goals
Learning Goals
The learning outcomes of the course are:
• Obtain a solid background in fundamental concepts of probability and statistical inference.
• Know the general statistical inference theory of classical and Bayesian approaches.
• Know how to use and apply the classic and modern methods of statistical inference.
• Apply the knowledge acquired in the study of new models, namely in the deduction and/or understanding of their parameters estimators as well the statistical inference associated with them.
• Ability to communicate ideas and scientific knowledge, in oral or written form, involving the use and/or interpretation of the concepts of statistical inference.
• Obtain a solid background in fundamental concepts of probability and statistical inference.
• Know the general statistical inference theory of classical and Bayesian approaches.
• Know how to use and apply the classic and modern methods of statistical inference.
• Apply the knowledge acquired in the study of new models, namely in the deduction and/or understanding of their parameters estimators as well the statistical inference associated with them.
• Ability to communicate ideas and scientific knowledge, in oral or written form, involving the use and/or interpretation of the concepts of statistical inference.
Contents
• Fundamental concepts of probability: measure and probability, bayes theorem, random vectors, marginal and conditioned distributions, expected values, Laplace transform and generator functions, random vector functions and transformations, stochastic convergences and limit theorems.
• Sample distributions and point estimation: methods of moments, maximum likelihood and least squares. Properties of estimators.
• Classical interval estimation: methods of obtaining interval estimators and properties.
• Classic hypothesis tests: duality and error types, likelihood ratio tests, test properties.
• Bayesian statistical inference: a priori and posteriori distributions. Bayesian point and interval estimation: credibility and maximum density intervals a posteriori.
• Bayesian hypothesis testing: model comparison criteria; bayes factor and most likely posterior model.
• Sample distributions and point estimation: methods of moments, maximum likelihood and least squares. Properties of estimators.
• Classical interval estimation: methods of obtaining interval estimators and properties.
• Classic hypothesis tests: duality and error types, likelihood ratio tests, test properties.
• Bayesian statistical inference: a priori and posteriori distributions. Bayesian point and interval estimation: credibility and maximum density intervals a posteriori.
• Bayesian hypothesis testing: model comparison criteria; bayes factor and most likely posterior model.
Teaching Methods
The curricular unit is organized in theoretical-practical classes. The classes are plenary and are based on the deduction, understanding and interpretation of the various statistical techniques always fostering a critical attitude and scientific rigor in the students. The introduction of theoretical concepts will be done by using application examples covering various areas.
Assessment
During the regular assessment period, students can choose between continuous and final assessments.
Students should prioritize the continuous assessment system, which involves taking individual, closed-book mini-tests. The course grade will be calculated by averaging (rounded to a whole number) the scores obtained in each mini-test. If students choose the final assessment system, they will be required to take an exam that considers all syllabus content.
In other assessment periods (reserve, special, or extraordinary), students are assessed using the final assessment system, taking an exam that considers all syllabus content.
Students should prioritize the continuous assessment system, which involves taking individual, closed-book mini-tests. The course grade will be calculated by averaging (rounded to a whole number) the scores obtained in each mini-test. If students choose the final assessment system, they will be required to take an exam that considers all syllabus content.
In other assessment periods (reserve, special, or extraordinary), students are assessed using the final assessment system, taking an exam that considers all syllabus content.
Teaching Staff
- Luís Miguel Lindinho da Cunha Mendes Grilo [responsible]
Certificações
