期刊
BERNOULLI
卷 28, 期 4, 页码 2606-2633出版社
INT STATISTICAL INST
DOI: 10.3150/21-BEJ1431
关键词
Central limit theorem; exponential concentration; partially observed diffusions; particle smoothing; pseudo-marginal methods; sequential Monte Carlo methods
资金
- Swedish Research Council [2018-05230]
- Swedish Research Council [2018-05230] Funding Source: Swedish Research Council
In this paper, we explore the online computation of expectations of additive state functionals under general path probability measures. We extend an existing algorithm using pseudo-marginalisation techniques, allowing it to be applied to different path-space Monte Carlo problems with linear complexity and constant memory requirements.
We consider online computation of expectations of additive state functionals under general path probability measures proportional to products of unnormalised transition densities. These transition densities are assumed to be intractable but possible to estimate, with or without bias. Using pseudo-marginalisation techniques we are able to extend the particle-based, rapid incremental smoother (PaRIS) algorithm proposed in [Bernoulli 23(3) (2017) 1951-1996] to this setting. The resulting algorithm, which has a linear complexity in the number of particles and constant memory requirements, applies to a wide range of challenging path-space Monte Carlo problems, including smoothing in partially observed diffusion processes and models with intractable likelihood. The algorithm is furnished with several theoretical results, including a central limit theorem, establishing its convergence and numerical stability. Moreover, under strong mixing assumptions we establish a novel O(n epsilon) bound on the asymptotic bias of the algorithm, where n is the path length and epsilon controls the bias of the transition-density estimators.
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