This paper proposes a new Sequential Monte Carlo algorithm to perform online estimation in the context of state space models when either the transition density of the latent state or the conditional likelihood of an observation given a state is intractable. In this setting, obtaining low variance estimators of expectations under the posterior distributions of the unobserved states given the observations is a challenging task. Following recent theoretical results for pseudo-marginal sequential Monte Carlo smoothers, a pseudo-marginal backward importance sampling step is introduced to estimate such expectations. This new step allows to reduce very significantly the computational time of the existing numerical solutions based on an acceptance-rejection procedure for similar performance, and to broaden the class of eligible models for such methods. For instance, in the context of multivariate stochastic differential equations, the proposed algorithm makes use of unbiased estimates of the unknown transition densities under much weaker assumptions than standard alternatives. The performance of this estimator is assessed for high-dimensional discrete-time latent data models, for recursive maximum likelihood estimation in the context of partially observed diffusion process, and in the case of a bidimensional partially observed stochastic Lotka-Volterra model.
翻译:本文提出一个新的序列蒙特卡洛算法,以便在潜伏状态的过渡密度或有条件的观测可能处于某种状态时,在状态空间模型的背景下进行在线估算。 在这种背景下,根据观测结果,在未观测到的状态的后方分布下获得低差异估计值是一项具有挑战性的任务。根据伪边际相继的蒙特卡洛光滑体的最新理论结果,将引入一个假偏差后向后向重要性取样步骤来估计这种预期值。这一新步骤将大大缩短基于类似性能的接受-拒绝程序的现有数字解决方案的计算时间,并扩大这类方法的合格模型类别。例如,在多变量相异式差异方程式中,拟议的算法对未知的过渡密度进行了不偏颇的估计,其假设比标准替代方法要弱得多。这一估计仪的性能被评估为高度离散时间潜值数据模型,在部分观测到的扩展过程中,以及在部分观测到的模型中,对二维空间部分观测到的多位数方位数。