Long-term stability of sequential Monte Carlo methods under verifiable conditions

By Randal Douc, Eric Moulines, Jimmy Olsson. 2012

49 citations recorded by the source corpus.

This paper discusses particle filtering in general hidden Markov models (HMMs) and presents novel theoretical results on the long-term stability of bootstrap-type particle filters. More specifically, we establish that the asymptotic variance of the Monte Carlo estimates produced by the bootstrap filter is uniformly bounded in time. On the contrary to most previous results of this type, which in general presuppose that the state space of the hidden state process is compact (an assumption that is rarely satisfied in practice), our very mild assumptions are satisfied for a large class of HMMs with possibly non-compact state space. In addition, we derive a similar time uniform bound on the asymptotic L-p error. Importantly, our results hold for misspecified models; that is, we do not at all assume that the data entering into the particle filter originate from the model governing the dynamics of the particles or not even from an HMM.

Subfields: Artificial Intelligence, Statistics and Probability, Probabilistic & Bayesian Methods

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Artificial Intelligence

In Statistics and Probability

In Probabilistic & Bayesian Methods

Citations in the corpus

Sequential Kernel Herding: Frank-Wolfe Optimization for Particle Filtering (2015, methodology): “The remaining 6 state-variables were tracked using a bootstrap particle ﬁlter with N = 200 particles; the strikingly small number of particles owing to the computational complexity of the likelihood evaluation.”