The DOI matches its Crossref record; 24 of the 24 references it cites were found in a registry or an index.
Curse-of-dimensionality revisited: Collapse of the particle filter in very large scale systems
Open accessAbstract
<!-- *** Custom HTML *** --> It has been widely realized that Monte Carlo methods (approximation via a sample ensemble) may fail in large scale systems. This work offers some theoretical insight into this phenomenon in the context of the particle filter. We demonstrate that the maximum of the weights associated with the sample ensemble converges to one as both the sample size and the system dimension tends to infinity. Specifically, under fairly weak assumptions, if the ensemble size grows sub-exponentially in the cube root of the system dimension, the convergence holds for a single update step in state-space models with independent and identically distributed kernels. Further, in an important special case, more refined arguments show (and our simulations suggest) that the convergence to unity occurs unless the ensemble grows super-exponentially in the system dimension. The weight singularity is also established in models with more general multivariate likelihoods, e.g. Gaussian and Cauchy. Although presented in the context of atmospheric data assimilation for numerical weather prediction, our results are generally valid for high-dimensional particle filters.
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Cited by
Obstacles to High-Dimensional Particle Filtering
Snyder, C., Bengtsson, T., Bickel, P., & Anderson, J. (2008) · Monthly Weather Review · doi:10.1175/2008mwr2529.1 · Cited by 696
Self-citationParticle Filtering in Geophysical Systems
van Leeuwen, P. J. (2009) · Monthly Weather Review · doi:10.1175/2009mwr2835.1 · Cited by 678
Integrating Crop Growth Models with Whole Genome Prediction through Approximate Bayesian Computation
Technow, F., Messina, C. D., Totir, L. R., & Cooper, M. (2015) · PLOS ONE · doi:10.1371/journal.pone.0130855 · Cited by 265
“The number of parameters we estimated was 404 (100 marker effects per physiological trait plus an intercept), which seems well beyond the dimensionality range for importance sampling [85].”
BackgroundFight sample degeneracy and impoverishment in particle filters: A review of intelligent approaches
Li, T., Sun, S., Sattar, T. P., & Corchado, J. M. (2014) · Expert Systems with Applications · doi:10.1016/j.eswa.2013.12.031 · Cited by 257
Metadata
- Authors
- Bengtsson, T., Bickel, P., & Li, B.
- Venue
- Institute of Mathematical Statistics Collections
- Publisher
- Institute of Mathematical Statistics
- Published
- 2008
- Pages
- 316-334
- OpenAlex
- W1628268552
- Cited by
- 397
- References
- 24
- FWCI
- 37.32
- Type
- book chapter
- Language
- en
- Open access
- green
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