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MCMC methods for sampling function space
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Stuart, A. M. (2008) MCMC methods for sampling function space. In: (MCQMC'08) Eighth International Conference on Monte Carlo and Quasi-Monte Carlo Methods in Scientific Computing, Montréal, Québec, 6-11 Jul 2008 (Unpublished)
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Official URL: http://www.iro.umontreal.ca/~lecuyer/mcqmc08/Progr...
Abstract
Applied mathematics is concerned with developing models with predictive capability, and with probing those models to obtain qualitative and quantitative insight into the phenomena being modelled. Statistics is data-driven and is aimed at the development of methodologies to optimize the information derived from data. The increasing complexity of phenomena that scientists and engineers wish to model, together with our increased ability to gather, store and interrogate data, mean that the subjects of applied mathematics and statistics are increasingly required to work in conjunction in order to significantly progress understanding. This talk is concerned with a research program at the interface between these two disciplines, aimed at problems in differential equations where profusion of data and the sophisticated model combine to produce the mathematical problem of obtaining information from a probability measure on function space. In this context there is an array of problems with a common mathematical structure, namely that the probability measure in question is a change of measure from a product measure. We illustrate the wideranging applicability of this structure, to problems in the atmospheric sciences, chemistry, econometrics and signal processing. For problems whose solution is determined by a probability measure on function space, information about the solution can be obtained by sampling from this probability measure. One way to do this is through the use of MCMC methods. We show how the common mathematical structure of the aforementioned problems can be exploited in the design of effective MCMC methods and we analyze the computational complexity of these methods.
Item Type: | Conference Item (Paper) | ||||
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Subjects: | Q Science > QA Mathematics | ||||
Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||
Official Date: | 8 July 2008 | ||||
Dates: |
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Status: | Not Peer Reviewed | ||||
Publication Status: | Unpublished | ||||
Conference Paper Type: | Paper | ||||
Title of Event: | (MCQMC'08) Eighth International Conference on Monte Carlo and Quasi-Monte Carlo Methods in Scientific Computing | ||||
Type of Event: | Conference | ||||
Location of Event: | Montréal, Québec | ||||
Date(s) of Event: | 6-11 Jul 2008 |
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