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The papers which develop SMC (eg. [1]) often begin by describing SIS. The two terms, SMC and SIS, don't seem to be synonyms. But neither does SIS seem to be just one "type" of SMC method. So how exactly do SIS and SMC fit together? Is SIS the basis or foundation for SMC?

[1] Del Moral, Pierre, Arnaud Doucet, and Ajay Jasra. "Sequential Monte Carlo samplers." Journal of the Royal Statistical Society: Series B (Statistical Methodology) 68.3 (2006): 411-436.

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I don't know if you still need help but just in case: SMC is basically SIS with resampling. It's quite a new area so people use different terms for the same thing. I believe that in case of this paper, in SMC they look only at the marginal distribution (so they integrate out the past) while in SIS they consider a space of increasing dimensions.
Here is a bit more about that: Difference between Sequential Importance Resampling and Sequential Monte Carlo.

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