1. Review of Basic Matrix Algebra (1.1 1. Vectors - Inner Product, Linear Independence, 1.2 2. Matrices - Partitioned Matrices, Symmetric Matrix, Inverse of Matrix, Determinants, Trace of Matrix, Orthogonal Matrix, Eigenvalues and Eigenvectors, Quadratic Forms, Spectral decomposition, Positive Definite and Non-Negative Definite Matrices, Square-Root Matrix)
2. Random Vectors and Matrices (2.1 1. Random Vectors and Matrices, 2.2 2. Mean Vector, Covariance Matrix, Correlation Matrix, Generalised Variance, 2.3 3. Mean Vector and Covariance matrix for Linear combination of Random variables, 2.4 4. Multivariate Data, Multivariate Random Sample, Sample Covariance and Sample Correlation Matrix, Generalised Sample Variance, Expected Values of Sample Mean and Covariance Matrix)
3. Multivariate Normal Distribution (3.1 1. Univariate and Bivariate Normal Density, 3.2 2. Multivariate Normal Distribution and Its Properties, Joint Moment Generating Function, 3.3 3. Distribution of Linear Combinations of Components of a Multivariate Random Vector, 3.4 4. Distribution of Subsets of components of a Multivariate Normal Random Vector, Zero Covariance and Independence, , 3.5 5. Distribution of X-m' S X-m , 3.6 6. Distribution of Linear Combination of Random Vectors, 3.7 7. Sampling Distributions of Mean and Sample Covariance Matrix, Wishart Distribution. , 3.8 8. Large Sample Behaviour of Mean and Sample Covariance, 3.9 Matrix)
4. Inferences about the Mean Vector (4.1 1. Hypothesis Testing of Mean Vector, 4.2 2. Hotelling’s T2 statistic, 4.3 3. Confidence Region for Mean Vector, 4.4 4. Simultaneous Confidence Interval or T2 interval, 4.5 5. Bonferroni Interval, 4.6 6. Large Sample Inferences, 4.7 7. Paired Comparisons, 4.8 8. Comparing Mean Vectors from Two Different Populations , 4.9 9. Simultaneous Confidence Intervals for the Differences in Mean Components)
5. Cluster Analysis (5.1 1.Introduction to Cluster Analysis, 5.2 2. Distance Measures and Similarity Coefficients for, 5.3 Pairs of Items, 5.4 3. Hierarchical Clustering Methods: Single Linkage, Complete Linkage, Average Linkage, Dendrograms, 5.5 4. Non-Hierarchical Clustering Method: K-means, 5.6 Method, , 5.7 5. Goodness of Fit for Dendrogram)
6. Discriminant Analysis (6.1 1. Introduction to Discriminant Analysis, 6.2 2. Minimum Expected Cost of Misclassification, 6.3 ECM Rule and Total Probability of Misclassification TPM Rule, , 6.4 3. Classification with Two Multivariate Normal Populations, 6.5 4. Fisher’s Approach to Classification with Two Populations, 6.6 5. Fisher’s Linear Discriminant Function, 6.7 6. Evaluating Classification Functions, 6.8 7. Optimum Error Rate OER, 6.9 8. Apparent Error Rate AER)
By the end of the course, students should be able to do the following:
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SCQF Level: 10
Credits: 15