# DEGREE REGULATIONS & PROGRAMMES OF STUDY 2015/2016

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DRPS : Course Catalogue : School of Mathematics : Mathematics

# Undergraduate Course: Research Topics in Statistics (MATH11171)

 School School of Mathematics College College of Science and Engineering Credit level (Normal year taken) SCQF Level 11 (Year 4 Undergraduate) Availability Available to all students SCQF Credits 10 ECTS Credits 5 Summary This course is recommended only for students who are confident in their ability to work at a more advanced level. This course aims to explore the wide range of applications of statistics with a selection of four topics, based on research interests of the staff being discussed within the course. The course will include use of R. Course description Examples of the topics to be discussed are given in the syllabus. Not all topics will be given each session. 1. Forensic statistics: The use of likelihood ratio or Bayes factor as a measure of the value of evidence will be introduced with various areas of application. Typical areas of application include the inference from for data from univariate and multivariate Normal distributions; DNA profiling; inference for data from finite populations; Bayes nets. 2. Modelling bioassay data from studies in entomology Modelling data on a disk; likelihood estimation and inference. Application to bioassay data. Brownian motion and bivariate Ornstein-Uhlenbeck diffusion models, mixture and hidden Markov models with applications; Bayesian estimation and inference. 3. Statistics in geosciences The structure and the use of the classical linear geostatistical model will be introduced in the context of modelling continuous spatial variation in environmental applications. Typical areas of application include the modelling of environmental processes such as temperature and rainfall, spatial interpolation and process mapping, and the prediction of key quantities of interest. 4. Statistics in medicine Introduction to pharmacokinetics via compartmental models and the statistical modelling of blood plasma concentration. Application to clinical trial data; estimation of maximum concentration level and average drug concentration over time; toxicity and dose determination. 5. Multivariate measures of association Copula modelling of random vectors and construction of multivariate probability models; higher-order dependence and measures of association; Kendall's, Spearman's and conditional Spearman's correlation measures; biplots; scale invariance; tail correlation. 6. Statistical inverse problems This course is on inverse problems where the unknown function is observed indirectly and with random error. Typical applications are in image processing such as image deblurring or tomography that is commonly used in medicine. Statistical techniques such as penalised likelihood approach and Bayesian estimators will be introduced, with application to image recovery, and convergence rates of these estimators will be studied. 7. Statistical challenges in large-scale physics experiments Modern physics experiments generate large amounts of data, with complex noise and signal properties, that pose a number of interesting statistical challenges. Some of the problems and proposed solutions in the ongoing efforts to detect gravitational waves will be described. 8. Bayesian hierarchical modelling for genomics data Genomics data is characterised by a large number of variables that are simultaneously observed in a small number of samples. After a brief introduction to Bayesian modelling, hierarchical Bayesian models will be constructed for this data. Hypothesis testing and estimation in a Bayesian framework will be applied to identifying genes relevant to various medical conditions. 9. Analysis of capture-recapture data Introduction to capture-recapture data - data collection process, encounter histories and m-arrays. Modelling assumptions, likelihood derivation and associated parameter estimation, with primary focus on survival probabilities. Application to real ecological datasets.
 Pre-requisites Students MUST have passed: Linear Statistical Modelling (MATH10005) AND Likelihood (MATH10004) AND Statistical Communication Skills (MATH10070) Co-requisites Prohibited Combinations Other requirements None
 Pre-requisites None High Demand Course? Yes
 Academic year 2015/16, Available to all students (SV1) Quota:  None Course Start Semester 2 Timetable Timetable Learning and Teaching activities (Further Info) Total Hours: 100 ( Lecture Hours 16, Seminar/Tutorial Hours 8, Programme Level Learning and Teaching Hours 2, Directed Learning and Independent Learning Hours 74 ) Assessment (Further Info) Written Exam 0 %, Coursework 100 %, Practical Exam 0 % Additional Information (Assessment) Coursework : 100% - four projects, one for each topic Feedback Not entered No Exam Information
 On completion of this course, the student will be able to: Expertise in four research areas of statistics.Appreciation of a formal strategy for statistical modelling.Awareness of areas of Statistics rarely studied at undergraduate level.Expertise in specialised software R packages and ability to run sample code.Development of problem solving techniques.
 This will be compiled each session according to the topics that are being covered.
 Graduate Attributes and Skills Not entered Keywords RTS
 Course organiser Dr Ioannis Papastathopoulos Tel: (0131 6)50 5020 Email: i.papastathopoulos@ed.ac.uk Course secretary Mrs Alison Fairgrieve Tel: (0131 6)50 5045 Email: Alison.Fairgrieve@ed.ac.uk
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