11396 - Multivariate Statistical Analysis

Academic Year 2014/2015

  • 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