The course in introductory to theory and applications of multivariate methods and models. In particular, the course includes the study of multivariate Gaussian distribution, multivariate regression, graphical models and exploratory multivariate analysis. The course includes the use of the software R.
Prerequisites
Statistical inference.
Teaching Methods
Lectures and labs.
Further information
.
Type of Assessment
Oral and written exam and students seminars.
Course program
1. Multivariate Gaussian distribution
Bivariate and multivarate distribution; marginal and conditional distributions
Correlation and marginal/conditional independence
Parameters estimators
Whishart and Hotelling T2 distribution
Hypothesis tests
Laboratory with R
2. Multivariate regression
Linear model
Estimators ad properties
Hypothesis tests and model selection
MANOVA and MANCOVA
Laboratory with R
3. Principal components analysis
Notation
Definition and properties of PCA
Uso ed interpretazione delle componenti principali
Laboratory with R
4. Introduction to graphical models
Non-directed graphs, directed acyclic and chain
Markov properties and factorization
Gaussian graphical models
Graphical log-linear models
5. Factor analysis
Introduction to exploratory factor
Rotation of axes
Interpretation of the factorial axes
Laboratory with R
Outline of confirmatory factor analysis
6. Discriminant analysis
Introduction to discriminant analysis
Maximum likelihood estimator
Linear discriminant analysis - Fisher's approach
Confusion matrix
Laboratory with R
7. Cluster Analysis
Introduction to the problem of classification
Distances and metrics
Hierarchical and nonhierarchical methods
Probabilistic and fuzzy methods
8. Introduction to causal inference
Rubin's counterfactual approach
- In experimental studies
- In observational studies
- Matching and Propensity Scores
Pearl’s Approach