Noise covariance matrices in state-space models: A survey and comparison of estimation methods-Part I

Nonlinear state-space models are ubiquitous in modeling real-world dynamical systems. Sequential Monte Carlo (SMC) techniques, also known as particle methods, are a well-known class of parameter estimation methods for this general class of state-space models. Existing SMC-based techniques rely on excessive sampling of the parameter space, which makes their computation intractable for large systems or tall data sets. Bayesian optimization techniques have been used for fast inference in state-space models with intractable likelihoods. These techniques aim to find the maximum of the likelihood function by sequential sampling of the parameter space through a single SMC approximator. Various SMC approximators with different fidelities and computational costs are often available for sample-based likelihood approximation. In this paper, we propose a multi-fidelity Bayesian optimization algorithm for the inference of general nonlinear state-space models (MFBO-SSM), which enables simultaneous sequential selection of parameters and approximators. The accuracy and speed of the algorithm are demonstrated by numerical experiments using synthetic gene expression data from a gene regulatory network model and real data from the VIX stock price index.

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ON COMPUTING THE CRAMER-RAO BOUND AND COVARIANCE MATRICES FOR PEM ESTIMATES IN LINEAR STATE SPACE MODELS

IFAC Proceedings Volumes ◽

10.3182/20060329-3-au-2901.00092 ◽

2006 ◽

Vol 39 (1) ◽

pp. 600-605 ◽

Cited By ~ 14

Author(s):

Torsten Söderström

Keyword(s):

State Space ◽

Covariance Matrices ◽

State Space Models ◽

Linear State ◽

Cramer Rao Bound

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Recursive parameter and state estimation methods for observability canonical state-space models exploiting the hierarchical identification principle

IET Control Theory and Applications ◽

10.1049/iet-cta.2018.6333 ◽

2019 ◽

Vol 13 (16) ◽

pp. 2538-2545 ◽

Cited By ~ 4

Author(s):

Ting Cui ◽

Feng Ding ◽

Ahmed Alsaedi ◽

Tasawar Hayat

Keyword(s):

State Estimation ◽

State Space ◽

State Space Models ◽

Estimation Methods ◽

Hierarchical Identification ◽

Canonical State

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Parameterizing state–space models for infectious disease dynamics by generalized profiling: measles in Ontario

Journal of The Royal Society Interface ◽

10.1098/rsif.2010.0412 ◽

2010 ◽

Vol 8 (60) ◽

pp. 961-974 ◽

Cited By ~ 32

Author(s):

Giles Hooker ◽

Stephen P. Ellner ◽

Laura De Vargas Roditi ◽

David J. D. Earn

Keyword(s):

Infectious Disease ◽

Differential Equations ◽

State Space ◽

Statistical Inference ◽

Deterministic Model ◽

State Space Models ◽

Control Measures ◽

Estimation Methods ◽

Deterministic Models ◽

Transmission Pathways

Parameter estimation for infectious disease models is important for basic understanding (e.g. to identify major transmission pathways), for forecasting emerging epidemics, and for designing control measures. Differential equation models are often used, but statistical inference for differential equations suffers from numerical challenges and poor agreement between observational data and deterministic models. Accounting for these departures via stochastic model terms requires full specification of the probabilistic dynamics, and computationally demanding estimation methods. Here, we demonstrate the utility of an alternative approach, generalized profiling, which provides robustness to violations of a deterministic model without needing to specify a complete probabilistic model. We introduce novel means for estimating the robustness parameters and for statistical inference in this framework. The methods are applied to a model for pre-vaccination measles incidence in Ontario, and we demonstrate the statistical validity of our inference through extensive simulation. The results confirm that school term versus summer drives seasonality of transmission, but we find no effects of short school breaks and the estimated basic reproductive ratio ℛ 0 greatly exceeds previous estimates. The approach applies naturally to any system for which candidate differential equations are available, and avoids many challenges that have limited Monte Carlo inference for state–space models.

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