  Sequential Monte Carlo (SMC) methods are powerful tools for Bayesian
inference but suffer from requiring many particles for accurate estimates,
leading to high computational costs. We introduce persistent sampling (PS), an
extension of SMC that mitigates this issue by allowing particles from previous
iterations to persist. This generates a growing, weighted ensemble of particles
distributed across iterations. In each iteration, PS utilizes multiple
importance sampling and resampling from the mixture of all previous
distributions to produce the next generation of particles. This addresses
particle impoverishment and mode collapse, resulting in more accurate posterior
approximations. Furthermore, this approach provides lower-variance marginal
likelihood estimates for model comparison. Additionally, the persistent
particles improve transition kernel adaptation for efficient exploration.
Experiments on complex distributions show that PS consistently outperforms
standard methods, achieving lower squared bias in posterior moment estimation
and significantly reduced marginal likelihood errors, all at a lower
computational cost. PS offers a robust, efficient, and scalable framework for
Bayesian inference.
