On Particle Methods for Parameter Estimation in State-Space Models

By Nikolas Kantas, Arnaud Doucet, Sumeetpal S. Singh, Jan M. Maciejowski, Nicolas Chopin. 2014

478 citations recorded by the source corpus.

Nonlinear non-Gaussian state-space models are ubiquitous in statistics, econometrics, information engineering and signal processing. Particle methods, also known as Sequential Monte Carlo (SMC) methods, provide reliable numerical approximations to the associated state inference problems. However, in most applications, the state-space model of interest also depends on unknown static parameters that need to be estimated from the data. In this context, standard particle methods fail and it is necessary to rely on more sophisticated algorithms. The aim of this paper is to present a comprehensive review of particle methods that have been proposed to perform static parameter estimation in state-space models. We discuss the advantages and limitations of these methods and illustrate their performance on simple models.

Subfields: Artificial Intelligence, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/ca844daa7736fe4088c84ec80bcedb13ae3074ed

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Citations in the corpus

Learning deep dynamical models from image pixels (2014, background): “, 2011), see also the recent survey (Kantas et al., 2015).”
Particle Value Functions (2017, methodology): “Lastly, the policy gradient of There are particle methods that would address the estimation of this score, e.g. (Kantas et al., 2015), but for large T the estimate suffers from high mean squared errors.”
Fusing Physics-based and Deep Learning Models for Prognostics (2020, methodology): “Some examples of popular estimation methods include iterative reweighted least-squares schemes [25], unscented Kalman filters (UKF) [29–31], particle filters [32], and Bayesian inference methods using Markov chain Monte Carlo [25,33].”
A Review of Innovation-Based Methods to Jointly Estimate Model and Observation Error Covariance Matrices in Ensemble Data Assimilation (2018, background): “This feedback process leads to filter divergence, as was pointed out by Pham et al. (1998), Anderson and Anderson (1999) or Anderson (2007).”
Nonlinear System Identification: A User-Oriented Road Map (2019, background): “Tutorial overviews of how to identify nonlinear state-space models using SMC are provided by [157], [158].”
Statistical Inference for Partially Observed Markov Processes via the R Package pomp (2015, background): “Arulampalam et al. (2002), Doucet and Johansen (2009), and Kantas et al. (2015) have written excellent introductory tutorials on the particle ﬁlter and particle methods more generally.”
A framework for quantifying the value of vibration-based structural health monitoring (2022, methodology): “More speciﬁcally, we implement an on-line particle ﬁlter [52], which performs Gaussian mixture (GM)-based [53] resampling [54] whenever the eﬀective sample size drops below a user-deﬁned threshold (step 8 in the algorithmic summary of Section 5).”