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APTS module: Nonparametric Smoothing

Module leader: A W Bowman and L Evers

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

Aims: The term `nonparametric smoothing' refers to a wide range of methods which allow data to be modelled flexibly. The course will start with the simplest case of density estimation and progress through standard forms of nonparametric regression to state-of-the art modelling tools which can be applied in a wide variety of settings. The course will cover the main ideas from a conceptual perspective as well as investigating aspects of the underlying theory and computation. There will also be some exploration of practical use of the methods in real applications.

Learning outcomes: By the end of the module, students will: understand the techniques of kernel density estimation and nonparametric regression, with data from one or more dimensions; appreciate the issues of bias and variance associated with model fitting and selection; be aware of the range of mechanisms which can be used to smooth data; understand how these techniques can be incorporated into wider modelling tools; be able to use these methods in a wide range of applications.

Prerequisites: Linear models, including a Bayesian approach (Modelling); generalised linear models (Modelling); R programming (preliminary APTS material); Taylor series expansions and basic concepts of asymptotic properties (Asymptotics); matrix computations (Statistical Computing).

Topics:

  • kernel approaches to density estimation and regression;
  • spline and basis approaches;
  • computational issues;
  • an insight into asymptotic properties;
  • nonparametric regression;
  • generalised additive models;
  • alternative approaches, including Gaussian processes;
  • case studies.

Assessment: A set of exercises assigned by the module leader, including a data-analysis exercise involving practical use of some of the methods covered.