This course covers the advanced theory of point estimation, interval estimation and hypothesis testing. Using a mathematically-oriented approach, the course provides a formal treatment of inferential problems, statistical methodologies and their underlying theory. It is suitable in particular for students intending to further their studies or to develop a career in statistical research. Contents include: (1) Decision problem – frequentist approach: loss function; risk; decision rule; admissibility; minimaxity; unbiasedness; Bayes’ rule; (2) Decision problem – Bayesian approach: prior and posterior distributions, Bayesian inference; (3) Estimation theory: exponential families; likelihood; sufficiency; minimal sufficiency; completeness; UMVU estimators; information inequality; large-sample theory of maximum likelihood estimation; (4) Hypothesis testing: uniformly most powerful (UMP) test; monotone likelihood ratio; UMP unbiased test; conditional test; large-sample theory of likelihood ratio; confidence set; (5) Nonparametric inference; bootstrap methods.

Assessment: coursework (40%) and examination (60%)

This course aims to give students an introduction on modern computationally intensive methods in statistics, with a strong focus on Bayesian methods. The role of computation as a fundamental tool in data analysis and statistical inference will be emphasized. The course will introduce topics including the generation of random variables, optimization techniques, and numerical integration using quadrature and Monte Carlo methods. This course will then cover the fundamental Bayesian framework, including prior elicitation, posterior inference and model selection. For posterior computation, Monte Carlo methods such as importance sampling and Markov chain Monte Carlo will be introduced. Methods for approximate inference such as variational Bayes will also be covered. Advanced Bayesian modeling with nonparametric Bayes will then be explored, with applications in machine learning. This course is particularly suitable for students who intend to pursue further studies or a career in research.

Assessment: coursework (50%) and examination (50%)

This course covers statistical concepts and tools involved in modelling data which are correlated in space. Applications can be found in many fields including epidemiology and public health, environmental sciences and ecology, economics and others. Covered topics include: (1) Outline of three types of spatial data: point-level (geostatistical), areal (lattice), and spatial point process. (2) Model-based geostatistics: covariance functions and the variogram; spatial trends and directional effects; intrinsic models; estimation by curve fitting or by maximum likelihood; spatial prediction by least squares, by simple and ordinary kriging, by trans-Gaussian kriging. (3) Areal data models: introduction to Markov random fields; conditional, intrinsic, and simultaneous autoregressive (CAR, IAR, and SAR) models. (4) Hierarchical modelling for univariate spatial response data, including Bayesian kriging and lattice modelling. (5) Introduction to simple spatial point processes and spatio-temporal models. Real data analysis examples will be provided with dedicated R packages such as geoR.

Assessment: coursework (50%) and examination (50%)

In many disciplines the basic data on an experimental unit consist of a vector of possibly correlated measurements. Examples include the chemical composition of a rock; the results of clinical observations and tests on a patient; the household expenditures on different commodities. Through the challenge of problems in a number of fields of application, this course considers appropriate statistical models for explaining the patterns of variability of such multivariate data. Topics include: multiple, partial and canonical correlation; multivariate regression; tests on means for one-sample and two-sample problems; profile analysis; test for covariances structure; multivariate ANOVA; principal components analysis; factor analysis; discriminant analysis and classification.

Assessment: coursework (40%) and examination (60%)

Many social and medical studies, especially those involving questionnaires, contain large amounts of categorical data. Examples of categorical data include presence or absence of disease (yes / no), mode of transportation (bus, taxi, railway), attitude toward an issue (strongly disagree, disagree, agree, strongly agree). This course focuses on analyzing categorical response data with emphasis on hands-on training of analyzing real data using statistical software SAS. Consulting experience may be presented in the form of case studies. Topics include: classical treatments of contingency tables; measures of association; logistic linear models and log-linear models for binary responses; and log-linear models for Poisson means.

Assessment: coursework (50%) and examination (50%)

Discrete time series are integer-indexed sequences of random variables. Such series arise naturally in climatology, economics, finance, environmental research and many other disciplines. The course covers the statistical modelling and forecasting of time series. Topics may include stationary and nonstationary time series, ARMA models, identification based on autocorrelation and partial autocorrelation, GARCH models, goodness-of-fit, forecasting, and nonlinear time series modelling.

Assessment: coursework (50%) and examination (50%)

Statistical methodologies and applications in fields of medicine, clinical research, epidemiology, public health, biology and biomedical research are considered. The types of statistical problems encountered will be motivated by experimental data sets. Important topics include design and analysis of randomized clinical trials, group sequential designs and crossover trials; survival studies; diagnosis; risks; statistical analysis of the medical process.

Assessment: coursework (40%) and examination (60%)

With the rapid developments in computer and data storage technologies, the fundamental paradigms of classical data analysis are mature for change. Data mining techniques aim at helping people to work smarter by revealing underlying structure and relationships in large amounts of data. This course takes a practical approach to introduce the new generation of data mining techniques and show how to use them to make better decisions. Topics include data preparation, feature selection, association rules, decision trees, bagging, random forests and gradient boosting, cluster analysis, neural networks, introduction to text mining.

Assessment: coursework (100%)

This course aims to introduce various statistical models and methodology used in marketing research. Special emphasis will be put on marketing analytics and statistical techniques for marketing decision making including market segmentation, market response models, consumer preference analysis, conjoint analysis and extracting insights from text data. Contents include statistical methods for segmentation, targeting and positioning, statistical methods for new product design, text mining techniques and market response models.

Assessment: coursework (50%) and examination (50%)

The recent explosion of social media and the computerization of every aspect of life resulted in the creation of volumes of mostly unstructured data (big data): web logs, e-mails, videos, speech recordings, photographs, tweets and others. This course aims to provide students with knowledge and skills in big data analytics, especially natural language processing (NLP). Topics will include basic information retrieval, text classification, word embedding, neural networks, sequence models, encoder-decoder, transformer, contextualized world representation, and language model. Students are required to be familiar with Python programming.

Assessment: coursework (100%)

Structural Equation Modelling (SEM) is a general statistical modelling technique to establish relationships among variables. A key feature of SEM is that observed variables are understood to represent a small number of “latent constructs” that cannot be directly measured, only inferred from the observed measured variables. This course covers the theories of structural equation models and their applications. Topics may include path models, confirmatory factor analysis, structural equation models with latent variables, Sub-models including multiple group analysis, MIMIC model, second order factor analysis, two-wave model, and simplex model, model fitness, model identification, and Comparison with competing models.

Pre-requisites: Pass in STAT7005 Multivariate methods or equivalent

Assessment: coursework (50%) and examination (50%)

The six degrees of separation theorizes that human interactions could be easily represented in the form of a network. Examples of networks include router networks, the World Wide Web, social networks (e.g. Facebook or Twitter), genetic interaction networks and various collaboration networks (e.g. movie actor coloration network and scientific paper collaboration network). Despite the diversity in the nature of sources, the networks exhibit some common properties. For example, both the spread of disease in a population and the spread of rumors in a social network are in sub-logarithmic time. This course aims at discussing the common properties of real networks and the recent development of statistical network models. Topics may include common network measures, community detection in graphs, preferential attachment random network models, exponential random graph models, models based on random point processes and the hidden network discovery on a set of dependent random variables.

Assessment: coursework (100%)