Cotter, S. L. and Roberts, G. O. and Stuart, A. M. and White, D. (2012) *MCMC methods for functions modifying old algorithms to make them faster.* Statistical Science . (Submitted)

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## Abstract

Many problems arising in applications result in the need

to probe a probability distribution for functions. Examples include Bayesian nonparametric statistics and conditioned diffusion processes. Standard MCMC algorithms typically become arbitrarily slow under the mesh refinement dictated by nonparametric description of the unknown function. We describe an approach to modifying a whole range of MCMC methods which ensures that their speed of convergence is robust under mesh refinement. In the applications of interest the data is often sparse and the prior specification is an essential part of the overall modeling strategy. The algorithmic approach that we describe is applicable whenever the desired probability measure has density with respect to a Gaussian process or Gaussian random field prior, and to some useful non-Gaussian priors constructed through random truncation. Applications are shown in density estimation, data assimilation in fluid mechanics, subsurface geophysics and image registration. The key design principle is to formulate the MCMC method for functions. This leads to algorithms which can be implemented via minor modification of existing algorithms, yet which show enormous speed-up on a wide range of applied problems.

Item Type: | Article |
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Subjects: | D - G > General |

Research Groups: | Oxford Centre for Collaborative Applied Mathematics |

ID Code: | 1492 |

Deposited By: | Peter Hudston |

Deposited On: | 02 Mar 2012 07:44 |

Last Modified: | 02 Mar 2012 07:44 |

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