Trade-off between number of particles and snippet length in integrator snippet SMC

Determine the optimal trade-off between the number of seed particles N and the snippet length T in integrator snippet Sequential Monte Carlo algorithms, explicitly accounting for computational realities where integration along snippets can be parallelized efficiently while resampling is not easily parallelizable. Establish theoretical guidance that quantifies how N and T should be balanced to optimize accuracy and efficiency under such constraints.

Background

The paper introduces integrator snippet SMC methods that, for each seed particle, evolve a deterministic integrator trajectory (a snippet) of length T and then resample among all snippet states. Under a fixed computational budget, practitioners typically balance the number of seeds N and the snippet length T, and experiments in the paper often keep N(T+1) fixed to compare settings.

In the Discussion, the authors explicitly note that understanding this balance is an open problem. They emphasize that snippet integration is well-suited to parallel hardware, whereas resampling is not, making standard complexity arguments delicate. A rigorous analysis would guide how to select N and T to best exploit parallelism while controlling estimator variance and computational cost.