  Over the years, sequential Monte Carlo (SMC) and, equivalently, particle
filter (PF) theory has gained substantial attention from researchers. However,
the performance of the resampling methodology, also known as offspring
selection, has not advanced recently. We propose two deterministic offspring
selection methods, which strive to minimize the Kullback-Leibler (KL)
divergence and the total variation (TV) distance, respectively, between the
particle distribution prior and subsequent to the offspring selection. By
reducing the statistical distance between the selected offspring and the joint
distribution, we obtain a heuristic search procedure that performs superior to
a maximum likelihood search in precisely those contexts where the latter
performs better than an SMC. For SMC and particle Markov chain Monte Carlo
(pMCMC), our proposed offspring selection methods always outperform or compare
favorably with the two state-of-the-art resampling schemes on two models
commonly used as benchmarks from the literature.
