2024
Complements of Probability and Statistics
Name: Complements of Probability and Statistics
Code: MAT14242L
6 ECTS
Duration: 15 weeks/156 hours
Scientific Area:
Mathematics
Teaching languages: Portuguese
Languages of tutoring support: Portuguese
Presentation
This UC aims to strengthen basic training in Probability and Statistics with the study of univariate and multivariate probability distributions, stochastic convergences, transformations of variables and random vectors, complementary hypothesis tests, and linear additive models.
Sustainable Development Goals
Learning Goals
Objectives:
It is intended to strengthen the basic training in Probability and Statistics with the complement of fundamental knowledge of probability theory and statistical theory.
Skills:
Know and use different concepts and basic statistical tools in statistical theory and its application areas.
Important to know different probabilistic models in statistical modeling.
Know and apply the basic principles of simple analysis of variance.
Be able to implement and analyze, in a critical way, a multilinear regression model.
It is intended to strengthen the basic training in Probability and Statistics with the complement of fundamental knowledge of probability theory and statistical theory.
Skills:
Know and use different concepts and basic statistical tools in statistical theory and its application areas.
Important to know different probabilistic models in statistical modeling.
Know and apply the basic principles of simple analysis of variance.
Be able to implement and analyze, in a critical way, a multilinear regression model.
Contents
- Complements of the Probability and Statistics theory: univariate probability distributions (Gamma, Beta and Weibull, among others) and multivariate, joint and conditional moments.
- Stochastic convergences, boundary distributions and some important inequalities.
- Transformations of variables and random vectors.
- Complements of hypothesis testing: more powerful test, Neyman-Pearson Lema, likelihood ratio tests.
- Linear additive models: definitions, exponential family and its properties, link function. Simple and multiple linear regression model (estimation, adjustment, validation and forecast).
- Stochastic convergences, boundary distributions and some important inequalities.
- Transformations of variables and random vectors.
- Complements of hypothesis testing: more powerful test, Neyman-Pearson Lema, likelihood ratio tests.
- Linear additive models: definitions, exponential family and its properties, link function. Simple and multiple linear regression model (estimation, adjustment, validation and forecast).
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 various statistical techniques always fostering a critical attitude and scientific rigor in students. Introduction of theoretical concepts using application examples covering various areas.
The evaluation is recommended to be continuous through the realization of two frequencies and one evaluation works with resolution of exercises, incentivizing the bibliographic research, the study by diverse sources and the acquisition of the theoretical concepts through a dedicated study.
The evaluation is recommended to be continuous through the realization of two frequencies and one evaluation works with resolution of exercises, incentivizing the bibliographic research, the study by diverse sources and the acquisition of the theoretical concepts through a dedicated study.
Teaching Staff (2023/2024 )
- Jorge Maurício Salazar Serrano [responsible]
