Obstacles to High-Dimensional Particle Filtering

By C. Snyder, Thomas Bengtsson, Peter J. Bickel, Jeffrey L. Anderson. 2008

743 citations recorded by the source corpus.

Subfields: Atmospheric Science, Global and Planetary Change

View Paper: https://www.semanticscholar.org/paper/30a811d3e137ff8d77662265612a67a9cd2fd273

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In Atmospheric Science

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Citations in the corpus

A Non-Gaussian Ensemble Filter Update for Data Assimilation (2010, background): “There have been several studies of how the different types of ﬁlters perform with nonlinear models (Lawson and Hansen 2004; Leeuwenburgh et al. 2005; Sakov and Oke 2008a,b; Sun et al. 2009; Mitchell and Houtekamer 2009).”
Nonlinear data assimilation in geosciences: an extremely efficient particle filter (2010, background): “…problem, the so-called ‘curse of dimensionality’, which is related to the fact that it is very unlikely that a swarm of model runs, called particles, shooting at random through state space will end up close to a large set of observations in a large-dimensional system (Snyder et al. , 2008).”
A Moment Matching Ensemble Filter for Nonlinear Non-Gaussian Data Assimilation (2011, background): “of the state space is moderately high (Snyder et al. 2008).”
Beyond Gaussian Statistical Modeling in Geophysical Data Assimilation (2010, background): “To prove this, Snyder et al. (2008) studied the statistics of the biggest weight.”
An exploration of the equivalent weights particle filter (2013, background): “It is still a serious issue in particle filtering whilst computer capabilities limit the number of particles that can be used (Snyder et al., 2008).”
Reconstructing surface temperature changes over the past 600 years using climate model simulations with data assimilation (2010, background): “However, fully exploring this state space would require a prohibitively high number of simulations [e.g., Lorenz , 1969; Van den Dool , 1994; Nicolis , 1998; Snyder et al. , 2008].”
Gaussian anamorphosis extension of the DEnKF for combined state parameter estimation: Application to a 1D ocean ecosystem model (2012, background): “However, the size of the ensemble required for an efficient application of such a filter is too large to be considered for realistic configurations (Snyder et al., 2008).”
On the stability of sequential Monte Carlo methods in high dimensions (2011, background): “target, as the dimension of the state grows to infinity then one requires, for some stability properties, a number of particles which grows exponentially in dimension (or ‘effective dimension’ in [48]); the algorithm considered is standard importance sampling.”
Data Assimilation: A Mathematical Introduction (2015, background): “Unfortunately, these filters can behave poorly in high dimensions [17, 9, 103].”
Error Bounds and Normalising Constants for Sequential Monte Carlo Samplers in High Dimensions (2014, background): “Recently (see [2], [4], and [24]) it was shown that some IS methods do not stabilise, in an appropriate sense, as the dimension of target densities in a particular class grows, unless N grows exponentially fast with dimension d.”
Climate model dependence and the replicate Earth paradigm (2013, methodology): “We note here that model weights obtained from 255 particle filter approximations to Bayes’ theorem (van Leeuwen, 2011; Snyder et al., 2008) share this 256 feature.”
A local particle filter for high-dimensional geophysical systems (2015, background): “Snyder et al. (2008) note that when either the model dimension or observation count is large, the PF requires significantly more particles to give an adequate representation of the system.”