2023
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, English
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.
Evaluation:
In the continuous evaluation regime, two compulsory works will be carried out, each counting 25% of the final grade and a test counting 50% of the final grade.
If not approved in continuous assessment, the student takes a final exam.
Evaluation:
In the continuous evaluation regime, two compulsory works will be carried out, each counting 25% of the final grade and a test counting 50% of the final grade.
If not approved in continuous assessment, the student takes a final exam.
Teaching Staff
- Gonçalo João Costa Jacinto [responsible]
