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  \textbf{\Large{\textsc{STANFORD UNIVERSITY}}}\\[5pt]
  \textbf{\Large{\textsc{DEPARTMENT OF STATISTICS}}}\\[5pt]
  \Large{\textsc{DEPARTMENTAL SEMINAR}}
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  4:15pm, Tuesday, November 6, 2007\\
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  Sequoia Hall Room 200\\
  (Cookies at 3:45 in 1st Floor Lounge)
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  \textsl{Peter Bickel} \\
  Department of Statistics\\
  UC Berkeley
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  \subsection*{Collapse of Particle Filters}
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\noindent

It has been widely realized that Monte Carlo methods (approximation via a sample ensemble) may fail in large scale systems. We offer some theoretical insight into this phenomenon in the context of   particle filters.In particular we will argue that (in a vanilla situation) collapse. meaning that the estimated posterior distribution concentrates on one point ,will occur unless the ensemble size grows super exponentially in the "effective dimension",a concept we will define.

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