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DRPS : Course Catalogue : School of Mathematics : Mathematics

Undergraduate Course: Research Topics in Statistics (MATH11171)

Course Outline
SchoolSchool of Mathematics CollegeCollege of Science and Engineering
Credit level (Normal year taken)SCQF Level 11 (Year 4 Undergraduate) AvailabilityAvailable to all students
SCQF Credits10 ECTS Credits5
SummaryThis 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.
Entry Requirements (not applicable to Visiting Students)
Pre-requisites Students MUST have passed: Linear Statistical Modelling (MATH10005) AND Likelihood (MATH10004) AND Statistical Communication Skills (MATH10070)
Prohibited Combinations Other requirements None
Information for Visiting Students
High Demand Course? Yes
Course Delivery Information
Not being delivered
Learning Outcomes
On completion of this course, the student will be able to:
  1. Demonstrate expertise in four research areas of statistics.
  2. Appreciate a formal strategy for statistical modelling.
  3. Show awareness of areas of Statistics rarely studied at undergraduate level.
  4. Demonstrate expertise in specialised software R packages and ability to run sample code.
  5. Develop problem solving techniques.
Reading List
This will be compiled each session according to the topics that are being covered.
Additional Information
Graduate Attributes and Skills Not entered
Course organiserDr Ioannis Papastathopoulos
Tel: (0131 6)50 5020
Course secretaryMrs Alison Fairgrieve
Tel: (0131 6)50 5045
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