Stochastic Analysis Seminar
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Mon, 09/10/2006 14:15 |
Professor Gregory Miermont (Universite Paris XI) |
Stochastic Analysis Seminar  |
DH 3rd floor SR |
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Mon, 09/10/2006 15:45 |
Professor Martin Barlow (UBC Canada) |
Stochastic Analysis Seminar |
DH 3rd floor SR |
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Mon, 16/10/2006 14:15 |
Prof Liming Wu (Universite Blaise Pascal-Clermont-Ferrand II) |
Stochastic Analysis Seminar |
DH 3rd floor SR |
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Mon, 16/10/2006 15:45 |
Dr Stanislav Volkov (University of Bristol) |
Stochastic Analysis Seminar |
DH 3rd floor SR |
/notices/events/abstracts/stochastic-analysis/mt06/volkov.shtml
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Mon, 23/10/2006 14:15 |
Dr Nigel Newton (University of Essex) |
Stochastic Analysis Seminar |
DH 3rd floor SR |
The talk will describe recent collaborative work between the speaker and Professor Sanjoy Mitter of MIT on connections between continuous-time nonlinear filtering theory, and nonequilibrium statistical mechanics.
The study of nonlinear filters from a (Shannon) information- theoretic viewpoint reveals two flows of information, dubbed 'supply' and 'dissipation'. These characterise, in a dynamic way, the dependencies between the past, present and future of the signal and observation processes. In addition, signal and nonlinear filter processes exhibit a number of symmetries, (in particular they are jointly and marginally Markov), and these allow the construction of dual filtering problems by time reversal. The information supply and dissipation processes of a dual problem have rates equal to those of the original, but with supply and dissipation exchanging roles. The joint (signal-filter) process of a nonlinear filtering problem is unusual among Markov processes in that it exhibits one-way flows of information between components.
The concept of entropy flow in the stationary distribution of a Markov process is at the heart of a modern theory of nonequilibrium statistical mechanics, based on stochastic dynamics. In this, a rate of entropy flow is defined by means of time averages of stationary ergodic processes.
Such a definition is inadequate in the dynamic theory of nonlinear filtering. Instead a rate of entropy production can be defined, which is based on only the (current) local characteristics of the Markov process. This can be thought of as an 'entropic derivative'. The rate of entropy production of the joint process of a nonlinear filtering problem contains an 'interactive' component equal to the sum of the information supply and dissipation rates.
These connections between nonlinear filtering and statistical mechanics allow a certain degree of cross- fertilisation between the fields. For example, the nonlinear filter, viewed as a statistical mechanical system, is a type of perpetual motion machine, and provides a precise quantitative example of Landauer's Principle. On the other hand, the theory of dissipative statistical mechanical systems can be brought to bear on the study of sub-optimal filters. On a more philosophical level, we might ask what a nonlinear filter can tell us about the direction of thermodynamic time.
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Mon, 23/10/2006 15:45 |
Professor Christophe Sabot (ENS Lyon) |
Stochastic Analysis Seminar |
DH 3rd floor SR |
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Mon, 30/10/2006 14:15 |
Dr Sarah Dance (University of Reading) |
Stochastic Analysis Seminar |
DH 3rd floor SR |
Numerical weather prediction
models require an estimate of the current state of the atmosphere as an initial
condition. Observations only provide partial information, so they are usually
combined with prior information, in a process called data assimilation. The
dynamics of hazardous weather such as storms is very nonlinear, with only a
short predictability timescale, thus it is important to use a nonlinear,
probabilistic filtering method to provide the initial conditions.
Unfortunately, the state space is
very large (about 107 variables) so approximations have to be made.
The Ensemble Kalman
filter (EnKF) is a quasi-linear filter that has
recently been proposed in the meteorological and oceanographic literature to
solve this problem. The filter uses a forecast ensemble (a Monte Carlo sample)
to estimate the prior statistics. In this talk we will describe the EnKF framework and some of its strengths and weaknesses. In
particular we will demonstrate a new result that not all filters of this type
bear the desired relationship to the forecast ensemble: there can be a
systematic bias in the analysis ensemble mean and consequently an accompanying
shortfall in the spread of the analysis ensemble as expressed by the ensemble
covariance matrix. This points to the need for a
restricted version of the notion of an EnKF. We have
established a set of necessary and sufficient conditions for the scheme to be
unbiased. Whilst these conditions are not a cure-all and cannot deal with
independent sources of bias such as modelling errors,
they should be useful to designers of EnKFs in the future.
/notices/events/abstracts/stochastic-analysis/mt06/dance.shtml
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Mon, 30/10/2006 15:45 |
Professor Francois Bolley (Université de Toulouse) |
Stochastic Analysis Seminar |
DH 3rd floor SR |
/notices/events/abstracts/stochastic-analysis/mt06/bolley.shtml
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Mon, 06/11/2006 14:15 |
Dr Nina Snaith (University of Bristol) |
Stochastic Analysis Seminar |
L1 |
/notices/events/abstracts/stochastic-analysis/mt06/snaith.shtml
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Mon, 06/11/2006 15:45 |
Professor Chris Rogers (University of Cambridge) |
Stochastic Analysis Seminar |
L1 |
/notices/events/abstracts/stochastic-analysis/mt06/rogers.shtml
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Mon, 13/11/2006 14:15 |
Prof Mihail Zervos (LSE) |
Stochastic Analysis Seminar |
DH 1st floor SR |
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Mon, 13/11/2006 15:45 |
Professor Kurt Johansson (KTH Stockholm) |
Stochastic Analysis Seminar |
DH 3rd floor SR |
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Mon, 20/11/2006 14:15 |
Professor Nina Gantert (Universitat Munster) |
Stochastic Analysis Seminar |
DH 3rd floor SR |
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Mon, 20/11/2006 15:45 |
Professor Helyette Geman (Birkbeck University) |
Stochastic Analysis Seminar |
DH 3rd floor SR |
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Mon, 27/11/2006 14:15 |
Dr Neil O'Connell (University of Cork) |
Stochastic Analysis Seminar |
DH 3rd floor SR |
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Mon, 27/11/2006 15:45 |
Professor Marta Sanz-Sole (Universitat de Barcelona) |
Stochastic Analysis Seminar |
DH 3rd floor SR |
/notices/events/abstracts/stochastic-analysis/mt06/sanz-sole.shtml
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