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In this paper the authors list advantages of SMC. One of them is:

Unlike MCMC, SMC particles are uncorrelated and do not require the determination of a burn-in period or assessment of convergence.

However, I believe that they are not uncorrelated after the resampling. Could someone help me understand why they would be uncorrelated?

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There seems to be a misunderstanding in your question. In SMC, you start with a sample $X^{1:n}$ and you transform it into a sample $\tilde{X}^{1:n}$ which is approximately from the target distribution. So, there is no burn-in, nor correlation, nor chain involved.

See:

http://www-irma.u-strasbg.fr/~guillou/meeting/cappe.pdf

http://www2.warwick.ac.uk/fac/sci/statistics/staff/academic-research/johansen/talks/20090309.pdf

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  • $\begingroup$ I believe the question related to things like the bootstrap particle filter. In that case, for 100 particles, 50 might share the same history for $t\leq T$, even though there states at $t=T+1$ differ. So "correlated" may refer to cloned essentially? $\endgroup$ – GeoMatt22 Aug 24 '16 at 23:38
  • $\begingroup$ @GeoMatt22: yes, we might call them cloned. Cloned seem to be correlated for me but maybe I'm wrong. $\endgroup$ – Paula Aug 25 '16 at 7:00

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