- Docente: Cristina Puzzarini
- Credits: 6
- SSD: MAT/06
- Language: Italian
- Moduli: Cristina Puzzarini (Modulo 1) Massimo Marcaccio (Modulo 2)
- Teaching Mode: Traditional lectures (Modulo 1) Traditional lectures (Modulo 2)
- Campus: Ravenna
- Corso: Second cycle degree programme (LM) in Environmental Assessment and Management (cod. 8418)
Learning outcomes
At the end of the course, the student knows several topics in Applied Multivariate Statistical Analysis. She/He can use the tools of multivariate normal distribution for inference on population means, Multivariate analysis of Variance, Discriminant analysis, Multivariate regression, cluster analysis by means of hierarchical methods and multidimensional scaling, PCA and factor analysis.
Course contents
• Data Organization. Sample multivariate descriptic
statistics
• Similarity and distance measures. Cluster analysis with
aggregation methods.
• Classical Multidimensional scaling
• Random vectors and matrices. Mean vector and covariance matrix.
Linear combinations of random vectors. Expected values and sample
covariance matrix. Generalized and total sample variance
• Normal multivariate distribution. Density function and
fundamental propertie. Mean and covariance sample distributions.
Large samples. Tests on normality. Transformation to normality.
• T2 di Hotelling. Confidence region and simultaneous confidence
intervals for the mean vector of a normal distribution.
• Paired comparisons. MANOVA with Wilks and Bartlett tests.
• Separation and classification of two normal populations. Fischer
discriminant analysis.
• Classical multivariate regression model. Least squares
estimation (BLUE). Confidence intervals for the estimates. Model
evaluation. Regression for new predictive variables.
• Principal component analysis (PCA). Analysis of data
variability. Data reduction and compression of images.
• Orthogonal factor model. Factor analysis by means of PCA and
maximum likelyhood method. Model validation. Evaluation of factors.
Readings/Bibliography
Applied Multivariate Statistical Analysis, R. A. Johnson e D. W. Wichern, Prentice Hall, V edizione, 2002
Teaching methods
Classroom lectures and computer lab sessions.
Assessment methods
Oral examination plus computer-lab exercise (about 70-75 minutes in
total)
Teaching tools
1) Blackboard (lectures and exercises) and video-projector. Lecture
notes
2) computational lab praticals
Office hours
See the website of Cristina Puzzarini
See the website of Massimo Marcaccio