Curse-of-dimensionality revisited : Collapse of importance sampling in very large scale systems

@inproceedings{Li2005CurseofdimensionalityR,
  title={Curse-of-dimensionality revisited : Collapse of importance sampling in very large scale systems},
  author={Bo Li and Thomas Bengtsson and Peter Bickel},
  year={2005}
}
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 a particle filter (as well as in general importance samplers), we demonstrate that the maximum of the weights associated with the sample ensemble members converges to one as both sample size and system dimension tends to infinity. Under fairly weak assumptions, this convergence is shown to… CONTINUE READING
13 Citations
25 References
Similar Papers

References

Publications referenced by this paper.
Showing 1-10 of 25 references

Some theory of Fisher’s linear discriminant function, ‘naive Bayes’, and some alternatives when there are many more variables than observations

  • P. J. Bickel, E. Levina
  • Bernoulli
  • 2004
1 Excerpt

Winds from a Bayesian hierarchical model: Computation for atmosphere-ocean research

  • T. Hoar, R. Milliff, D. Nychka, C. Wikle, L. Berliner
  • Journal of Computational and Graphical Statistics
  • 2003
1 Excerpt

Similar Papers

Loading similar papers…