Skip to main content

Trinity College Dublin, The University of Dublin

Trinity Menu Trinity Search

School of Mathematics

You are here Courses > Undergraduate > Courses & Modules

Module ST3456: Modern statistical methods II

Credit weighting (ECTS)
5 credits
Semester/term taught
Hilary term 2012-13
Contact Hours
11 weeks, 3 lectures including tutorials per week
Lecturer
Professor Simon Wilson
Learning Outcomes
On successful completion of this module students should be able to
  • Derive the structure function from the structure diagram of a system;
  • Prove results on system reliability in terms of the reliability of their components;
  • Define and interpret the failure rate and derive the survival function from it;
  • Fit lifetime distributions to data, including censored data;
  • Calculate non-parametric estimates of the survival function;
  • Calculate various exceedances and the distribution of the maxima and minima of a sequence of random variables;
  • State the extreme value theorem and apply it to derive approximate distributions of extremes;
  • Use the bootstrap (both parametric and non-parametric) and jacknife to derive approximate confidence intervals and bias of estimates;
  • State the advantages and disadvantages of the bootstrap and jacknife;
Module Content
  • Survival Analysis: systems of components, reliability of systems, failure rate, lifetime distributions, inference, censoring;
  • Extreme Value Theory: modelling extrema, extreme value theorem, inference, extrema under non-random and random censoring;
  • The Bootstrap: review of Monte Carlo simulation, the jacknife, the simple bootstrap, extensions;
 
Module Prerequisite
ST2351
Recommended Reading
Barlow, R.E. and Proschan, F. (1981), Statistical Theory of Reliability and Life Testing, 2nd edition. To Begin With.
Crowder, M.J., Kimber, A.C., Smith, R.L. and Sweeting, T.J. (1991), Statistical Analysis of Reliability Data. Chapman & Hall
Reiss, R-D and thomas, M. (1991), Statistical Analysis of Extreme Values.
Efron, B. and Tibshirani, R. (1994), An Introduction to The Bootstrap, Chapman & Hall
Tanner, M. (1997), Tools For Statistical Inference. Springer
Assessment Detail
This module will be examined jointly with ST3455 in a 3-hour examination in Trinity term, except that those taking just one of the two modules will have a 2 hour examination.