Sequential Monte Carlo refers to a class of algorithms particularly popular for inference in state space models. While SMC can be effective, for instance, in intractable filtering problems, it is known to encounter difficulties in the smoothing context, due to 'ancestral degeneracy’. Since ancestral degeneracy is often the key performance-limiting factor, it is of interest to quantify this problem. We have attempted to do so, via an asymptotic analysis of the genealogies induced by resampling.

I will begin with a gentle introduction to SMC methods and an explanation of how ancestral degeneracy arises, before presenting asymptotic results describing the genealogies of various SMC algorithms.