20410440 - ST410-Introduction to Statistics

Introduction to the basics of mathematical statistics and data analysis, including quantitative numerical experiments using suitable statistical software.

Curriculum

teacher profile | teaching materials

Fruizione: 20410555 ST410-STATISTICA in Scienze Computazionali LM-40 DE OLIVEIRA STAUFFER ALEXANDRE

Programme

Introduction to statistics: random sampling of finite and infinite populations. Definition of the statistical model and the concept of statistics. Example of statistics. Properties of statistics: sufficient, minimal and complete statistics.

Point estimators: method of moments, maximum likelihood estimators and Bayes estimators. EM algorithm.

How to evaluate estimators: bias, consistency and mean square error. UMVU estimators and efficient estimators.

Confidence interval: the concept of pivotals, asymptotic methods and the delta method.

Hypothesis testing: definitions, likelihood ratio test and duality with confidence interval. Uniformly most powerful tests.

Non-parametric methods: Goodness-of-fit test for discrete and continuum variables, contingency tables and Kolmogorov-Smirnov test.

Other topics: analysis of variance (ANOVA), linear regression, generalized linear regression and logistic regression.


Core Documentation

Statistical Inference
Casella e Berger
Duxbury
2nd edition.


Type of delivery of the course

Lectures with exercises during the lectures and a project for the analysis of real data. In case the emergency situation due to COVID-19 persists, lectures will be delivered through the platform Teams, with notes available from the platform Moodle. There will also be regular homeworks.

Attendance

Attendance of lectures is recommended.

Type of evaluation

Final written exam with questions of conceptual and numerical nature. Homeworks. A project for the analysis of real data (in groups of 2 or 3 students), to apply the methods studied during the lectures. In case the emergency situation due to COVID-19 persists, the final written exam may be replaced with an oral exam.

teacher profile | teaching materials

Fruizione: 20410555 ST410-STATISTICA in Scienze Computazionali LM-40 DE OLIVEIRA STAUFFER ALEXANDRE

Programme

Introduction to statistics: random sampling of finite and infinite populations. Definition of the statistical model and the concept of statistics. Example of statistics. Properties of statistics: sufficient, minimal and complete statistics.

Point estimators: method of moments, maximum likelihood estimators and Bayes estimators. EM algorithm.

How to evaluate estimators: bias, consistency and mean square error. UMVU estimators and efficient estimators.

Confidence interval: the concept of pivotals, asymptotic methods and the delta method.

Hypothesis testing: definitions, likelihood ratio test and duality with confidence interval. Uniformly most powerful tests.

Non-parametric methods: Goodness-of-fit test for discrete and continuum variables, contingency tables and Kolmogorov-Smirnov test.

Other topics: analysis of variance (ANOVA), linear regression, generalized linear regression and logistic regression.


Core Documentation

Statistical Inference
Casella e Berger
Duxbury
2nd edition.


Type of delivery of the course

Lectures with exercises during the lectures and a project for the analysis of real data. In case the emergency situation due to COVID-19 persists, lectures will be delivered through the platform Teams, with notes available from the platform Moodle. There will also be regular homeworks.

Attendance

Attendance of lectures is recommended.

Type of evaluation

Final written exam with questions of conceptual and numerical nature. Homeworks. A project for the analysis of real data (in groups of 2 or 3 students), to apply the methods studied during the lectures. In case the emergency situation due to COVID-19 persists, the final written exam may be replaced with an oral exam.