11396 - Multivariate Statistical Analysis

Learning outcomes

Learning outcomes: knowledge of several topics in Applied Multivariate Statistical Analysis and capability to use the tools of Multivariate normal distribution for inference on population means, Multivariate analysis of Variance, Discriminant analysis, Multivariate regression, Cluster analysis, Prinicipal component analysis, and factor analysis.

Course contents

•Principles of R

• Data Organization. Sample multivariate descriptic statistics

• 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

• Random Samples and the Expected Values of the Sample Mean and Covariance Matrix. Generalized Variance.

• Normal multivariate distribution: from the univariate to the multivariate case, fundamental properties and Contours of constant density. Multivariate Normal Likelihood. Large samples. Tests on normality: Q-Q plot. Transformation to normality.

• T2 di Hotelling: statistical hypotheses and level of significance, from the t-student to the T2 test. Confidence region and simultaneous confidence intervals for the mean vector of a normal distribution. Large samples. Charts for Monitoring a Sample of Individual Multivariate Observations for Stability.

• Paired comparisons. Comparing Mean Vectors from Two Populations. Comparing Several Multivariate Population Means: from ANOVA to MANOVA (with Wilks test).

• Classical multivariate regression model. Least squares estimation. 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.

• Similarity and distance measures. Cluster analysis with aggregation methods.

• Introduction to the machine learning systems: neural networks, evolutionary algorithms.

Readings/Bibliography

Applied Multivariate Statistical Analysis, R. A. Johnson e D. W. Wichern, Prentice Hall, V edizione, 2002

Introduzione alla chemiometria, Tedeschi Roberto, Edises, 1998

Metodi Statistici per la Sperimentazione Biologica, A. Camussi, F. Möller, E. Ottaviano, M. Sari Gorla, Zanichelli, II edizione, 1995.

Teaching methods

Classroom lectures and practical computer sessions.

As concerns the teaching methods of this course unit, all students must attend Module 1, 2 on Health and Safety online:

https://elearning-sicurezza.unibo.it/?lang=en

https://www.unibo.it/en/services-and-opportunities/health-and-assistance/health-and-safety/online-course-on-health-and-safety-in-study-and-internship-areas

Assessment methods

Oral examination plus computer-practical exercise.

Teaching tools

Blackboard (lectures and exercises) and video-projector.

Computational laboratory practicals

Lecture notes.

Office hours

See the website of Assimo Maris