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
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.
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.
This module aims to give students a grounding in the use of statistical software for data manipulation, analysis and simulation in R.
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.
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.
This course is a showcase for how the various branches of physics come together to give rise to real life phenomena. Using the example of stars, we will revisit a wide range of different physics and see how the various ingredients interact and thus how all branches of physics play a role in creating the fundamental building blocks of the universe. The emphasis of the course is on the more theoretical aspects of physics. The course is compulsory for ‘with Astronomy’ students but offers a good opportunity for all Physics students who want to obtain a hands-on experience of ‘the bigger picture’ in physics.
The module will start with an introductory session on common research techniques used in Biomedical Science. This will be followed by sessions covering the following topics: 1. Pluripotent stem cells (2 sessions) 2. Neural stem cells 3. Musculoskeletal stem cells (2 sessions) 4. Cancer stem cells 5. Ethics (2 sessions) The sessions will combine a seminar and general discussion to clarify any points and to frame any questions arising from the lecture that the students find interesting. Prior to each topic, a relevant primary research publication and supporting documentation that exemplifies research in the subject area will be provided. Students should read the paper prior to attending the session and pay particular attention to the methods section to ensure they are familiar with the basic principles of the techniques and/or any confusing abbreviations used. Methodological queries will be discussed at the session. For topics 1 and 3, one or more students, depending on class numbers, will be designated to prepare an oral presentation on a selected paper for the following week. The presentation will comprise the paper and background questions arising from the article or the seminar. All students will be expected to join in the discussion of the paper during and after the presentation, although only those students who are presenting will be assessed. Presenting students will be expected to research other articles to introduce concepts in the paper. All students will be expected to research other articles to bring to the general discussion of the selected paper. For topics 2 and 4, all students will write a critical appraisal of the selected paper stating the hypothesis and summarising the background, results and conclusions with comment on strengths, weaknesses and any new questions arising as a consequence of the paper. There will be no oral presentation for these topics. For topic 5, all students will participate in a discussion/debate.
Modern concerns like global warming and alternative fuels highlight the need for a STEM educated population. This module aims to provide a comprehensive overview of STEM education by examining current trends and best practices in the field. The module is designed to engage students in a hands-on and interdisciplinary approach to learning STEM subjects with a focus on Mathematics and Science. Topics to be covered include current trends in STEM education, theoretical frameworks in STEM education, real-world applications of STEM subjects, the use of games as a teaching tool and the benefits of informal learning.
This module with introduce synthetic organic methods in which other elements play a key role with an emphasis on stereo and regio selectivity.
The Stochastic OR Techniques part introduces the concepts and applications of the following four topics: queuing systems, inventory systems, reliability theory and decision theory. Models and examples are also given to demonstrate applications of the topics. Discrete event simulation is taught separately via lectures and computer workshops. One of the pre-requisites for MATH6013
