Statistical Methods and Applications

MAURIZIO VICHI

Learning goals
Knowing how to reorganize multidimensional data with a complex structure for their statistical analysis. Starting from the multivariate statistical methodologies, knowing how to realize complex strategies of analysis that have an easy interpretation. To be able to make decisions based on empirical evidence giving appropriate answers to corporate information requests. Knowing how to extract relevant information from large data (big data).

Knowledge and understanding
Knowledge of advanced multivariate statistical methodologies and advanced formal data analysis strategies with a model-based statistical approach.

Applying knowledge and understanding
Understanding the most appropriate complex techniques to be able to make decisions based on empirical evidence, respond to corporate information requests and be able to extract relevant information from the observed data.

Making judgements
Students develop critical skills through the application of complex multivariate statistical methodologies. They learn to critically interpret the results obtained by applying the procedures to real data sets.

Communication skills
Students, through the study and performance of practical exercises, acquire the technical-scientific language of the discipline, which must be used in the world of work. Communication skills are also developed through group activities.

Learning skills
Students who pass the exam have learned a method of analysis that allows them to face, the world of work having acquired advanced statistical analysis tools for complex and large data.

multivariate statistics

FORMATIVE OBJECTIVES
Know how to reorganize multidimensional data with a complex structure and analyze it using multivariate statistical methods with multiple objectives: co-clustering, clustering and dimensional reduction, regression and factor analysis by SEM.
To be able to make decisions based on empirical evidence giving appropriate answers to corporate information requests. Knowing how to extract relevant information from large data (big data).

Program
Short references to multivariate statistics. Unsupervised and supervised classification methodologies: Unsupervised classification of units (cluster analysis), Non-hierarchical methods; K-means, Pam, K-means fuzzy; single bond, average-linkage, complete linkage, centroid, Ward method; interpretation of the dendrogram, methods for choosing a partition; analysis of the main components (PCA); Factorial analysis; multiple regression with fixed or random effects; multivariate multiple regression.

Insights: K-means extensions for dissimilarity data; methods based on the likelihood: maximum likelihood clustering, maximum likelihood mixture clustering, EM (Gaussian models);
Choice of the number of clusters and parsimonious models through informational criteria; Evaluation of classification by bootstrap sampling; Parsimonious dendrograms; the Double K-means, extensions of the Double K-means; Analysis in disjunctive and non-negative principal components; Analysis of disjointed factors; Hierarchical analysis of disjointed factors to construct composite indicators,

Classification methodologies and joint dimensional reduction: Classification-Classification and Classification Analysis in disjoint principal components; Double K-means; the reduced K-means, the factorial K-mans; Structural equations model

Course notes and matlab algorithms
Suggested Books: G. McLachlan, D. Peel, (2000). Finite Mixture Models, Wiley Series in Probability and Statistics. A. C. Rencher, (2002). Methods of Multivariate Analysis, Wiley Series in Probability and Statistics; 2nd edition; A.D. Gordon (1999). Classification, Chapman & Hall, 2nd edition;
Softwares: SPSS, SAS

oral examination

3 times per week from October to December

oral and written examinations