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Details of Grant 

EPSRC Reference: EP/J01365X/1
Title: Sequential Monte Carlo methods for applications in high dimensions.
Principal Investigator: Fearn, Professor T
Other Investigators:
Researcher Co-Investigators:
Project Partners:
Department: Statistical Science
Organisation: UCL
Scheme: First Grant - Revised 2009
Starts: 01 July 2012 Ends: 30 June 2013 Value (£): 98,688
EPSRC Research Topic Classifications:
Statistics & Appl. Probability
EPSRC Industrial Sector Classifications:
No relevance to Underpinning Sectors
Related Grants:
Panel History:
Panel DatePanel NameOutcome
30 Jan 2012 Mathematics Prioritisation Panel Meeting January 2012 Announced
Summary on Grant Application Form
Sequential Monte Carlo (SMC) methods are nowadays routinely employed across a wide range of disciplines to calibrate mathematical models and carry out forecasting about complex non-linear stochastic systems, using information from incoming data. SMC methods have been successfully applied in such diverse areas as econometrics, communications, target tracking, computer vision, roboting and biology. They will infer about unknown parameters of stochastic systems and unobserved states of the systems (the "signal") given streams of data.

However, it is a common knowledge that standard SMC methods cannot tackle important high-dimensional problems, arising in fields such as atmospheric sciences, oceanography, hydrology and signal processing, as their computational cost has been found to increase exponentially fast with the dimension of the state space of the system.

The proposed research will investigate and develop advanced SMC methods of improved algorithmic efficiency in high dimensions, rendering SMC methodology practically relevant in such contexts. This is of high importance as alternative methods currently used in high dimensions cannot fully capture non-linear model dynamics arising in applications, and can give inaccurate estimates of uncertainty or forecasts in such non-linear scenarios.
Key Findings
A main objective of the funded project has been the investigation of the potential of a Monte-Carlo method (Sequential Monte-Carlo) in the context of high-dimensional inverse problems, with important applications in weather forecasting and data assimilation. We have indeed now developed such Monte-Carlo methods which can be appropriate for the problems at hand, and have shown analytical results from their application together with important theoretical findings in 3 submitted papers. We believe that our research on this problem could be very influential in the area of Monte-Carlo methods as it has gone against the common belief that such methods are not relevant for high-dimensional applications. The research during the Grant has opened up a number of interesting research routes which are now investigated in a number of projects with collaborators.
Potential use in non-academic contexts
No information has been submitted for this grant.
Impacts
No information has been submitted for this grant.
Sectors submitted by the Researcher
Education; Environment; Information & Communication Technologies
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