The module provides an introduction to statistical programming in R. The module consists of lectures and computer labs for students to gain hands-on experience of statistical programming.
The module covers methods of disclosure control for tabular data and microdata, and how the utility of the resulting data is traded off against the risk of disclosure.
Functions of one and several random variables are considered such as sums, differences, products and ratios. The central limit theorem is proved and the probability density functions are derived of those sampling distributions linked to the normal distribution. Bivariate and multivariate distributions are considered, and distributions of maximum and minimum observations are derived. This module is a pre-requisite for all subsequent statistics modules, and desirable for Actuarial Mathematics I and II and Simulation and Queues
Statistical genetics has played a pivotal role in the discovery of genes that cause disease in humans. This module introduces the basic concepts and terms in genetics and demonstrates the use of statistical models to identify disease genes in humans.
This module develops some mathematical foundations of statistical inference: the theory of learning from data under uncertainty. We begin by studying a selection of useful tools and techniques from probability theory, including moment generating functions and transformations of random variables. Then we proceed to explore fundamental methods for point estimation, interval estimation and hypothesis testing, with a particular emphasis on maximum likelihood theory. We also introduce the framework of Bayesian inference and discuss the frequentist and subjective interpretations of probability.
Statistical inference involves using data from a sample to draw conclusions about a wider population. Given a partly specified statistical model, in which at least one parameter is unknown, and some observations for which the model is valid, it is possible to draw inferences about the unknown parameters and hence about the population from which the sample is drawn. As such, inference underpins all aspects of statistics. However, inference can take different forms. It may be adequate to provide a point estimate of a parameter, i.e. a single number. More usually, an interval is required, giving a measure of precision. It may also be necessary to test a pre-specified hypothesis about the parameter(s). These forms of inference can all be considered as special cases of the use of a decision function. There are a number of different philosophies about how these inferences should be drawn, ranging from that which says the sample contains all the information available about a parameter (likelihood), through that which says account should be taken of what would happen in repeated sampling (frequentist), to that which allows the sample to modify prior beliefs about a parameter’s value (Bayesian). This Module aims to explore these approaches to parametric statistical inference, particularly through application of the methods to numerous examples.
Statistical learning and data science provide us with new forms of data and powerful new analysis tools. Advances in AI have allowed huge improvements in our ability to predict, but at the same time, these methods and data sources generate important ethical issues that we must consider. This module will provide students with the tools to appreciate the power of AI but also its limitations, and to be able to understand which AI tools might be suitable for particular tasks.
Statistical mechanics links the microscopic properties of physical systems to their macroscopic properties. Thermodynamics, which describes macroscopic properties, can then be derived from statistical mechanics with a few well motivated postulates. It leads to a microscopic interpretation of thermodynamic concepts, such as thermal equilibrium, temperature and entropy. In the course the basic principles of statistical mechanics will be introduced with applications to the physics of matter.
Statistical Methods for Finance is a critical module for you to learn basics for future modules on Econometrics, as well as their final year dissertation. This module covers important topics such as probability, discrete and random variables, Probability distributions, normal distribution, hypothesis testing, graphical analysis, correlation and simple regression. Lectures are followed by in-depth practical examples using tools that show the real world implications.
The main aim of the module is to provide the students with necessary knowledge of statistics and stochastic processes to carry out simple statistical procedures and to be able to develop simulation and other models widely employed in OR. The model is split into two parts: Statistics and Stochastic Processes.
Statistical Modelling I offers a comprehensive study of maximum likelihood estimation and multiple linear regression, covering both estimation and inferential procedures. The theoretical framework is formulated using vector and matrix methods. Techniques for model diagnostics, assessment of adequacy, and model selection are also covered.
Simple linear regression is developed for one explanatory variable using the principle of least squares. The extension to two explanatory variables raises the issue of whether both variables are needed for a well-fitting model, or whether one is sufficient and, if so, which one. These ideas are generalised to many explanatory variables (multiple regression), for which the necessary theory of linear models is developed in terms of vectors and matrices. Checking model adequacy is introduced, e.g. by examining plots of the residuals. Widening the class of models that can be considered by the use of dummy variables for qualitative explanatory variables to assess treatment effects. The methods are implemented using a suitable software and students gain experience and advice through weekly worksheets. One of the pre-requisites for MATH3012, MATH3013, MATH3014, MATH6021, MATH6025, MATH6027 and MATH6135
The module Statistical Modelling II covers in detail the theory of linear regression models, where explanatory variables are used to explain the variation in a response variable, which is assumed to be normally distributed. However, in many practical situations the data are not appropriate for such analysis. For example, the response variable may be binary, and interest may be focused on assessing the dependence of the probability of 'success' on potential explanatory variables. Such techniques are important in many disciplines such as finance, market research and medicine. Alternatively, a variety of biological and social science data are in the form of cross-classified tables of counts, called contingency tables. The structure of such tables can be examined to determine the pattern of interdependence of the cross-classifying variables.
This module aims to give students a grounding in the use of statistical software for data manipulation, analysis and simulation. It uses the R software as a basis, but also introduces students to the Python programming language, as both tools have wide functionality and close links with data science.
This module aims to give students a grounding in the use of statistical software for data manipulation and analysis in Python.
The Statistical Programming in R Module is focused on extending existing skills in analyzing data from quantitative research. The focus of this course will not be on extensively expanding the mathematical knowledge of the techniques employed but will be on acquiring practical skills such as scripting, flexible matrix manipulation and advanced visualization. All these skills are particularly useful when confronted with especially large datasets, and when confronted with a multitude of repetitive statistical procedures needing implementation. This module will also cover an introduction into Linear Mixed Models. Analyses will be implemented using the interactive programming environment known as R. R is a free, open source programming language for statistical analysis.
This module aims to give students a grounding in the use of statistical software for data manipulation, analysis and simulation in R.
The module is designed to prepare economics students for the econometrics modules taken in their second and third year. The module provides an introduction to the topic of statistics, with particular reference to the use of statistics to address questions in economics. The module content covers both descriptive statistics and statistical inference, leading up to regression analysis. The course content is typically as follows: describing data; probability; random variables; sampling; estimation; hypothesis testing; simple and multiple regression.
All economics students, on both single and joint honours programmes, take this course. It is optional for students outside of economics. The module is designed to prepare students for the econometrics modules taken in second and third year. It also complements the economics modules taken in by students in first and second year. It provides an introduction to the topic of statistics, with reference to economics examples. It then covers more advanced topics leading up to regression analysis. The course content is as follows: describing data; probability; discrete random variables; continuous random variables; sampling; estimation; hypothesis testing; simple regression and multiple regression. One of the pre-requisites for MATH2040, MATH3085, ECON1021, ECON2001, ECON2002, ECON2003, ECON2004, ECON2026 and ECON3016.
The module provides an overview of issues and ideas concerning the scope and organisation of Official Statistics and its processes and products, including Statistical Acts and Codes of Practice. The module provides a general foundation for the more detailed study of these elements and identifies links with other relevant disciplines
The module provides an overview of issues and ideas concerning the scope and organisation of Official Statistics and its processes and products, including Statistical Acts and Codes of Practice. The module provides a general foundation for the more detailed study of these elements and identifies links with other relevant disciplines.
The Statistics Project gives MSc students to conduct an in-depth study, either of a particular advanced statistical methodology, or of the application of one or more methods to real applied problems. The aim is to develop skills of organising work, identifying and directing your own work and writing a comprehensive report on a major piece of work. The choice of project is determined by the student's own interests and every student will benefit from one-to-one meetings with a supervisor, usually a member of academic staff.
