The aim of this course is twofold: to provide an overview of the most common statistical methods for multivariate analysis, and to provide the necessary information to solve the real world problems that are created due to several factors/characters/features/variables.

The main objective of this course are

to understand multivariate modeling based on real world problems;

to learn most common multivariate statistical methods for real world data analysis;

to develop the capability of multivariate model building strategies; and

Hands-on training on multivariate data analysis to understand how to provide the necessary information to solve the real world problems.

After completing this course successfully, the learners/students would be able

to analyze multivariate datasets to provide the necessary information to solve the real world problems that are associated with several factors/characters/features/variables;

to select the appropriate statistical algorithms for analyzing multivariate datasets;

to improve the existing statistical algorithms for analyzing multivariate datasets; and

to develop new statistical algorithms for analyzing multivariate datasets

Principal Component Analysis: Introduction, ML estimator of principal components (PCs) and their variances, Sampling properties, Hypothesis testing, Singular Value decomposition and its application, Application of PCs in regression analysis and clustering.

Factor Analysis: Introduction, Orthogonal factor model, Methods of estimation, Factor rotation and interpretation, Estimation factor scores, Testing goodness of fit, Application in regression, Clustering and Bayesian analysis.

Independent Component Analysis: Introduction, Information theory, Methods of ICA estimation, ICA algorithms.

Canonical Correlation Analysis: Introduction, Canonical correlation and varieties in population, and their estimation, Relationship with other correlation coefficients and linear regression analysis.

Classification: Basic principles, Classification with two or more populations using Bayes, Fisher’s and logistic classifiers, Evaluation of classifiers.

Clustering: Introduction, Similarity measures, Hierarchical clustering methods, Non-hierarchical clustering methods.

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