Monte Carlo Smoothing for Nonlinear Time Series

By Simon J. Godsill, Arnaud Doucet, Matthew West. Journal of the American Statistical Association, 2004

638 citations recorded by the source corpus.

We develop methods for performing smoothing computations in general state-space models. The methods rely on a particle representation of the filtering distributions, and their evolution through time using sequential importance sampling and resampling ideas. In particular, novel techniques are presented for generation of sample realizations of historical state sequences. This is carried out in a forward-filtering backward-smoothing procedure that can be viewed as the nonlinear, non-Gaussian counterpart of standard Kalman filter-based simulation smoothers in the linear Gaussian case. Convergence in the mean squared error sense of the smoothed trajectories is proved, showing the validity of our proposed method. The methods are tested in a substantial application for the processing of speech signals represented by a time-varying autoregression and parameterized in terms of time-varying partial correlation coefficients, comparing the results of our algorithm with those from a simple smoother based on the filtered trajectories.

Subfields: Artificial Intelligence, Oceanography, Signal Processing

View Paper: https://www.semanticscholar.org/paper/6fe3de760657c10e99f192733aeb68a42824e81f

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Citations in the corpus

General duality between optimal control and estimation (2008, background): “Some progress along these lines has been made [4].”
Dynamic Detection of Change Points in Long Time Series (2007, neutral): “In contrast the particle smoothers of Kitagawa (1996) and Godsill et al. (2004) require to store the whole set of particles at every iteration, but these are general methods while our approach is specific to change point models.”
Rao-Blackwellization of Particle Markov Chain Monte Carlo Methods Using Forward Filtering Backward Sampling (2011, background): “, [14]), and we discuss a cost/efficiency analysis of this approach in Section V and show in two examples that backward sampling with multiple trajectories can be notably more efficient than genealogical tracing.”
Policy Risk and the Business Cycle (2014, methodology): “This distribution can be formed from mass points, or particles, where δ is the Dirac delta function and ω it is the weight attached to the respective draw/particle σ it (Godsill et al., 2004).”
An efficient stochastic approximation EM algorithm using conditional particle filters (2013, methodology): “For instance, assume that we employ the forward filter/backward simulator particle smoother by [16] in PSEM.”
Monte Carlo filtering for multi target tracking and data association (2005, methodology): “It may also be possible to improve the performance of the SSPF by incorporating the temporal smoothing ideas of [45] and [ 46 ]: after sampling the targets sequentially in the forward direction, a backward smoothing run may be designed to further refine the sample representations for the individual ”
Smoothing algorithms for state–space models (2010, methodology): “(11) A similar idea was extended in Godsill et al. (2004) to sample from p(x 1:T |y 1:T ) using the related forward filtering-backward sampling formula.”
Particle methods for change detection, system identification, and control (2004, methodology): “Otherwise, when is large, one can use, for example, the forward filtering backward sampling algorithm [24].”
Estimating Macroeconomic Models: A Likelihood Approach (2007, positive): “We do so following the suggestion of Godsill, Doucet, and West (2004).”
Diffusion of Lexical Change in Social Media (2012, methodology): “To obtain smoothed estimates of η , we apply a sequential Monte Carlo (SMC) smoothing algorithm known as Forward Filtering Backward Sampling (FFBS) [30].”
Nested Sequential Monte Carlo Methods (2015, neutral): “It is possible to improve the performance of the algorithm by instead making use of a backward simulator (Godsill et al., 2004; Lindsten & Sch¨on, 2013) to simulate (cid:101) X 1: n .”
Particle gibbs with ancestor sampling (2014, methodology): “For further comparison, we also run an untruncated forward filter/backward simulator (FFBS) particle smoother (Godsill et al., 2004), using N = 10 000 particles and M = 1 000 backward trajectories, with a computational cost of O(NMT 2).”