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# APTS module: Computer Intensive Statistics

Module leader: R Everitt

Please see the full Module Specifications for background information relating to all of the APTS modules, including how to interpret the information below.

Aims: This module will introduce various computationally-intensive methods and their background theory, including material on simulation-based approaches such as Markov-chain Monte Carlo (MCMC) and the bootstrap, and on strategies for handling large datasets. The different methods will be illustrated by applications.

Learning outcomes: After taking this module, students will have a working appreciation of MCMC, the bootstrap and other simulation-based methods and of their limitations, and have some experience of implementing them for simple examples.

Prerequisites: Preparation for this module should include a review of:

• familiarity with basic types of convergence of random variables: in probability, almost sure and in distribution (as for example covered in Shiryaev, 1996; or Rosenthal, 2006);
• relevant basic material on statistical modelling (for which the earlier APTS module 'Statistical Modelling' would be advantageous; see also Davison, 2003);
• basic Markov chains (as for the 'Applied Stochastic Processes' module; relevant further reading can be found in Shiryaev, 1996);
• basic knowledge of programming in a high-level language such as R (R will be used for case studies and exercises). An introduction to R can be found here.

Further reading on prerequisite material:

• A. C. Davison (2003). Statistical Models. Cambridge University Press.
• J. S. Rosenthal (2006). A First Look at Rigorous Probability Theory, 2nd edition. World Scientific Publishing Co.
• A. N. Shiryaev (1996). Probability. Springer-Verlag, New York.

Topics:

• Overview of simulation-based inference; Monte Carlo testing.
• Basic theory of bootstrap methods; practical considerations; limitations.
• Basic theory of MCMC; types of MCMC samplers; assessment of convergence/mixing; other practical considerations; case studies.

Assessment: Exercises set by the module leader, which will include some practical simulation.