Computationally Intensive Methods

Module code: MD7443

This module will cover Bayesian and non-Bayesian computational models.

Topics covered

  • An introduction to the Likelihood analysis of a statistical model with several unknown parameters, considers the more controversial topic of hypothesis testing based on the likelihood and extends the use of maximum likelihood to more complex problems and looks at the statistics that can be derived from the results
  • How to apply splines and fractional polynomials when fitting non-linear functions including how to choose between models and plot the fitted functions
  • The ideas of bootstrapping and to be able to obtain confidence intervals for parameters in situations where it is difficult to obtain confidence intervals analytically
  • Missing data patterns, problems arising from missing data and the basic concepts of multiple imputation
  • The use of simulation in statistics and in particular for assessing the performance of statistical methods in terms of bias and convergence. In addition the use of simulation for complex power calculations
  • Bayesian Methods for multi-parameter problems
  • Markov chain Monte Carlo methods, proposal distributions, convergence monitoring, starting values and stopping times
  • Introduction to WinBUGS to fit a range of statistical models and interpretation of the findings

Learning

  • 20 hours of lectures
  • 28 hours of practical sessions
  • 102 hours of independent study

Assessment

  • Computer and problem-based exercises: multi-dimensional likelihood (25%)
  • Computer and problem-based exercises: simulation and modelling non-linear functions (25%)
  • Bayesian coursework (50%)