# Difference between Sequential Importance Resampling and Sequential Monte Carlo

I'm trying to understand this paper but I can't figure out what the difference between SIR and SMC is. I thought that SIR is an example of SMC but the authors seem to distinguish between them. They state:

In this section, we show how it is possible to use any local move—including MCMC moves— in the SIS framework while circumventing the calculation of distribution (9),

where (9) corresponds to the importance distribution. However, I don't see why this would be a problem in SIS and how SMC is different. I would be very grateful for help!

A standard reference on this topic is:

A tutorial on particle filtering and smoothing: Fifteen years later. Arnaud Doucet, Adam M Johansen

In particular:

So, as you can see, SMC = SIS + resampling, also known as SIR or SIS/R. This definition is also in the paragraph immediately after equation (1) in the paper your cited. The resampling step, as discussed in section 2.4 of the paper you cited, circumvents the need for calculating the importance distribution in SIS (the equation (9) you refer to), which is impossible to compute is most cases.

• Thank you. To sum up, SMC is the same as SIR. I think this is a reason why I found this article confusing because the authors use both notions. Commented Aug 7, 2016 at 11:15
• @Paula Indeed. SMC is a relatively young area, and some concepts and slang have been shaped recently. This is one of the reasons why the tutorial I posted is so popular (~1000 citations) since it puts together several ideas.
– Goro
Commented Aug 7, 2016 at 11:40

I disagree with the other answer. SMC is a term that encompasses algorithms that are not particle filters. The latter estimate sequences of state distributions assuming known parameters of a state space model. However, there exist SMC samplers that estimate posterior distributions of models that aren't even time series models.

Within many papers that deal exclusively with particle filtering, though, it is quite common to refer to particle filtering algorithms (such as SIR/SISR) as SMC algorithms. In my opinion, it sounds cooler, but it leads to this sort of confusion. It is easy to dig up a source on particle filtering that uses the terms interchangeably.

SIR/SISR both refer to the same thing, which is a particle filtering algorithm.

Edit: allow me to quote from the same reference mentioned above: