The purpose of this module is to provide the postgraduate student with the concepts, tools and techniques needed to undertake standard statistical analysis and to use these concepts to underpin their adoption of data mining techniques.
Linear Algebra
The definition of a matrix. Matrix algebra, including the addition and multiplication of matrices and multiplication by scalars. The representation of vectors as matrices. The definition of the determinant and the inverse for square matrices. Methods for calculating the inverse of a matrix, including the cofactor method and Gauss-Jordan elimination. Solving systems of linear equations using the inverse. Eigenvalues and eigenvectors.
Review of Descriptive Statistics
Calculation of mean, mode, median and standard deviation. Grouped data, calculation of class intervals, calculation of mean, mode, median and standard deviation for grouped data. Data representation and types of charts. Linear regression and correlation as geometric ideas and as data analysis techniques.
Probability
The definition of the fundamental ideas of events, experiments and probability. Independent events, conditional probabilities and the addition and multiplication laws. Permutations and combinations. The concepts of a random variable and its distribution, the definition of population parameters in terms of the probability distribution function and the cumulative probability distribution. Discrete and continuous probability distributions, including the exponential, normal, binomial and Poisson distributions. Examples of the role of these distributions in reliability prediction, component failures and designing for reliability.
Fundamentals of Hypothesis Testing
The concept of a Hypothesis test. The concept of a statistic. The common population parameters as statistics. The Central Limit Theorem and the concept of standard error. The role of the normal distribution arising from the Central Limit theorem. The representation of the results of a test; critical values and confidence intervals. The concept and limitations of a Hypothesis test, including type I and II errors and their probabilities.
Standard Hypothesis Tests
Distributions including the ‘Student t’, the chi-square and the F distributions. The F distribution as a ratio of chi-square distributions. Standard tests, including tests on means and variances, paired sample and unpaired tests on comparisons of means. Categorical tests using the chi-square distribution, such as goodness-of-fit tests to a distribution and tests for independence. Linear regression and correlation as statistical tests. The power of a statistical test. Effects sizes and the calculation of sample sizes. Reporting the results of an experiment and Hypothesis test, communicating the meaning of a test to peers and colleagues from non-technical backgrounds, interpreting existing reports and academic papers.
Multivariate Statistics
The design of experiments and the comparison of group means by one- and two-way analysis of variance (ANOVA). Relating an experiment to the form of the data collected. The type and nature of response variables and the concept of an attribute. Multiple regression and the General Linear Model. Easing of assumptions on the errors for generalised linear models. The General linear model as the foundation for Analysis of Variance and Analysis of Covariance, including Multivariate models (MANOVA, ANCOVA, MANCOVA)
Principal Component Analysis
Rotations and Orthogonal transformations. Eigenvalue decomposition. The eigenvectors of the covariance matrix, rotations and orthogonal transformations of the variables. Eigenvalue decomposition of the covariance matrix. The role of transformations in investigating attributes.
Bayesian inference
The Bayesian concept and method. The nature of priors. Bayesian testing. Comparison of Bayesian methods with Null Hypothesis based statistical testing. Large sample properties of Bayesian inference.
Parameter estimation
Parametric inference and the Maximum likelihood estimate. The maximum likelihood estimator and its properties, including asymptotic normality. The method of moments for parametric inference.
| Module Content & Assessment | |
|---|---|
| Assessment Breakdown | % |
| Other Assessment(s) | 100 |