Applied Statistics

Piercesare Secchi

Obiettivi e contenuti del corso

The course reviews several statistical concepts and methods for describing and analyzing mutivariate data. The aim is twofold: first, to provide students with the mathematical knowledge necessary for making proper interpretations, selecting appropriate techniques and understanding their strenghts and weaknesses, and second, to emphasize real life and engineering applications where multivariate statistical methods and modern computer packages permit to elicit information from multivariate data through rather complex satistical analyses.

Descrizione degli argomenti trattati

Exploring a multivariate dataset: descriptive statistics and graphical displays. The geometry of a multivariate sample. Generalized Variance. The metric induced by the covariance matrix.

Data representation and dimensional reduction: the analysis of the covariance structure, principal component analysis. Independent component analysis.

Inferences about a mean vector: Hotelling T^2 test. Confidence regions and simultaneous comparisons of component means. The Bonferroni method for multiple comparisons. Familywise Error Rate and False Discovery Rate. Comparisons of several multivariate means. ANOVA and MANOVA. Inference for Linear Models. Beyond Ordinary Least Squares: ridge regression, lasso, regularized least Squares. Introduction to generalized linear models.

Discrimination, classification, clustering: Statistical classification: model, misclassification costs and prior probability. Bayesian supervised classification and the Fisher approach to discriminant analysis. Alternative approaches to classification: logistic regression, CART. Similarity measures. Unsupervised classification; hierarchical and nonhierarchical methods. Multidimensional scaling.

Introduction to Functional Data Analysis. Data smoothing, dimensional reduction and representation. Functional principal component analysis. Data registration: phase and amplitude variability. Classification of functional data.

Statistics for spatial data. Random fields, variogram models and variogram fitting. Spatial prediction and Kriging, Functional data with spatial dependence.

Organizzazione del corso e modalità di verifica

Methods and algorithms will be illustrated in the lab sessions through applications to real data sets; analyses will be performed in R, an opensource package for the statistical analysis downloadable at www.r-project.org . Students are expected to work on a data analysis team project developed along the course.

The exam consists of three parts: a written exam, an oral exam and the presentation of the data analysis team project. To obtain a positive final mark for the course the student should pass with a grade greater than or equal to 18/30 each part of the exam; the final mark is then obtained as the weighted average of three grades, with weights respectively equal to 0.55 for the written exam, 0.20 for the oral exam and 0.25 for the project presentation.

Blibliografia

1. Johnson, R.A. e Wichern, D.W., (2007). Applied Multivariate Statistical Analysis (sixth edition), Prentice Hall, Upper Saddle River

2. Hastie, T., Tibshirani, R. e Friedman, J. (2009). The Elements of Statistical Learning: data mining, inference and prediction. (Second Edition), Springer-Verlag, New York.

3. Ramsay, J.O. e Silverman, B.W., (2005). Functional Data Analysis (second edition), Springer Series in Statistics, Springer, New York

4. Ramsay, J.O. e Silverman, B.W., (2002). Applied Functional Data Analysis: methods and case studies, Springer Series in Statistics, Springer, New York

5. Cressie, N. (1993). Statistics for Spatial Data (Revised Edition), John Wiley & Sons, New York

The exam consists of three parts: a written exam, an oral exam and the presentation of the data analysis team project. To obtain a positive final mark for the course the student should pass with a grade greater than or equal to 18/30 each part of the exam; the final mark is then obtained as the weighted average of three grades, with weights respectively equal to 0.55 for the written exam, 0.20 for the oral exam and 0.25 for the project presentation.