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| Titel |
Clever particle filters, sequential importance sampling and the optimal proposal |
| VerfasserIn |
Chris Snyder |
| Konferenz |
EGU General Assembly 2014
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| Medientyp |
Artikel
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| Sprache |
Englisch
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| Digitales Dokument |
PDF |
| Erschienen |
In: GRA - Volume 16 (2014) |
| Datensatznummer |
250100210
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| Publikation (Nr.) |
 EGU/EGU2014-16104.pdf |
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| Zusammenfassung |
| Particle filters rely on sequential importance sampling and it is well known that their
performance can depend strongly on the choice of proposal distribution from which
new ensemble members (particles) are drawn. The use of clever proposals has
seen substantial recent interest in the geophysical literature, with schemes such as
the implicit particle filter and the equivalent-weights particle filter. Both these
schemes employ proposal distributions at time tk+1 that depend on the state at tk
and the observations at time tk+1. I show that, beginning with particles drawn
randomly from the conditional distribution of the state at tk given observations
through tk, the optimal proposal (the distribution of the state at tk+1 given the
state at tk and the observations at tk+1) minimizes the variance of the importance
weights for particles at tk overall all possible proposal distributions. This means
that bounds on the performance of the optimal proposal, such as those given by
Snyder (2011), also bound the performance of the implicit and equivalent-weights
particle filters. In particular, in spite of the fact that they may be dramatically more
effective than other particle filters in specific instances, those schemes will suffer
degeneracy (maximum importance weight approaching unity) unless the ensemble size
is exponentially large in a quantity that, in the simplest case that all degrees of
freedom in the system are i.i.d., is proportional to the system dimension. I will also
discuss the behavior to be expected in more general cases, such as global numerical
weather prediction, and how that behavior depends qualitatively on the observing
network.
Snyder, C., 2012: Particle filters, the "optimal" proposal and high-dimensional systems.
Proceedings, ECMWF Seminar on Data Assimilation for Atmosphere and Ocean., 6-9
September 2011. |
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