Fast and Numerically Stable Particle-Based Online Additive Smoothing: The AdaSmooth Algorithm

We present a novel sequential Monte Carlo approach to online smoothing of additive functionals in very general class path-space models. Hitherto, the solutions proposed literature suffer from either long-term numerical instability due particle-path degeneracy or, case that is remedied by particle approximation so-called backward kernel, high computational demands. In order balance optimally speed against stability, we propose furnish (fast) naive smoother, propagating recursively sample particles and associated statistics, with an adaptive backward-sampling-based updating rule which allows number (costly) samples be kept at minimum. This yields new, function-specific algorithm, AdaSmooth, computationally fast, numerically stable easy implement. The algorithm provided rigorous theoretical results guaranteeing its consistency, asymptotic normality stability as well demonstrating empirically clear superiority AdaSmooth existing algorithms. Supplementary materials for this article are available online.