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

  title={Curse-of-dimensionality revisited : Collapse of importance sampling in very large scale systems},
  author={Bo Li and Thomas Bengtsson and Peter Bickel},
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
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