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Module Descriptor School of Computer Science and Statistics

Module CodeST3455
Module NameModern Statistical Methods I
Module Short TitleN/a
Semester TaughtMichaelmas
Contact HoursLecture hours: 33Lab hours: 0Tutorial hours: 0Total hours: 33
Module PersonnelLecturing staff: Simon Wilson
Learning Outcomes

At the end 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-parameteric) and jacknife to derive approximate confidence intervals and bias of estimates;
  • State the advantages and disadvantages of the bootstrap and jacknife.
Learning Aims

This module will describe several topics of a more advanced nature in probabilty modelling and statistics

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

Recommended Reading List

Barlow, R.E. and Proschan, F. (1981), Statistical Theory of Reliability and Life Testing, 2nd edition.

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. Birkha ̈user.

For the bootstrap: Efron, B. and Tibshirani, R. (1994), An Introduction to The Bootstrap. Chapman & Hall.

For the EM algorithm: Tanner, M. (1997) Tools For Statistical Inference. Springer.

Module PrerequisitesST2351, ST2352
Assessment Details

Assessment is by a 2 hour written examination. To pass the module, students must achieve an overall mark of 40%.

Module Website
Academic Year of DataN/a