Prior information in structure estimation

Kárný, Miroslav; Nedoma, Petr; Khaylova, N.; Pavelková, Lenka

doi:10.1049/ip-cta:20030861

Cited by 12 publications

(10 citation statements)

References 5 publications

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“…which is obtained with the help of operation of marginalization, chain rule [5], Proposition (2.1) and Dirac delta. All the pdfs in (15) are known from models (1)- (2). After integrating and some algebraic rearrangements the proposed form of Z(d 1 |x 0 ) provides the initial state, conditional only on the prior knowledge f (y 0 , u 0 , y 1 , u 1 ), while the state x 1 is being integrated out.…”

Section: Prior Knowledge Elicitationmentioning

confidence: 99%

Prior knowledge processing for initial state of Kalman filter

Suzdaleva

2009

Adaptive Control & Signal

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The paper deals with a specification of the prior distribution of the initial state for Kalman filter. The subjective prior knowledge, used in state estimation, can be highly uncertain. In practice, incorporation of prior knowledge contributes to a good start of the filter. The present paper proposes a methodology for selection of the initial state distribution, which enables eliciting of prior knowledge from the available expert information. The proposed methodology is based on the use of the conjugate prior distribution for models belonging to the exponential family. The normal state-space model is used for demonstrating the methodology. The paper covers processing of the prior knowledge for state estimation, available in the form of simulated data. Practical experiments demonstrate the processing of prior knowledge from the urban traffic control area, which is the main application of the research.

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Section: Prior Knowledge Elicitationmentioning

confidence: 99%

Prior knowledge processing for initial state of Kalman filter

Suzdaleva

2009

Adaptive Control & Signal

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“…The prior pdf f 0 ≡ f ( |V 0 ) should quantify all prior knowledge [19]. It delimits primarily the domain where the estimated lies with a high probability.…”

Section: Choice Of the Alternative Vmentioning

confidence: 99%

“…Additional analysis and experiments indicate that f ∞ = f for f , f in the CEF. Irrespective of this i → 0.5 (19). This made us to use its changes in the proposed stopping rule.…”

mentioning

confidence: 99%

Use of Kullback–Leibler divergence for forgetting

Kárný

Andrýsek

2008

Adaptive Control & Signal

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Non-symmetric Kullback-Leibler divergence (KLD) measures proximity of probability density functions (pdfs). Bernardo (Ann. Stat. 1979; 7(3):686-690) had shown its unique role in approximation of pdfs. The order of the KLD arguments is also implied by his methodological result. Functional approximation of estimation and stabilized forgetting, serving for tracking of slowly varying parameters, use the reversed order. This choice has the pragmatic motivation: recursive estimator often approximates the parametric model by a member of exponential family (EF) as it maps prior pdfs from the set of conjugate pdfs (CEF) back to the CEF. Approximations based on the KLD with the reversed order of arguments preserves this property. In the paper, the approximation performed within the CEF but with the proper order of arguments of the KLD is advocated. It is applied to the parameter tracking and performance improvements are demonstrated. This practical result is of importance for adaptive systems and opens a way for improving the functional approximation.

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“…The papers [14,18,19] proposed the desired elicitation technique that transforms knowledge into fictitious data, i.e. data that could be observed on a modelled system, and uses this data for the estimation as the real one.…”

Section: Introductionmentioning

confidence: 99%

Fully probabilistic knowledge expression and incorporation

Kárný

Guy

Kracík³

et al. 2014

Statistics and Its Interface

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An exploitation of prior knowledge in parameter estimation becomes vital whenever measured data is not informative enough. Elicitation of quantified prior knowledge is a well-elaborated art in societal and medical applications but not in the engineering ones. Frequently required involvement of a facilitator is mostly unrealistic due to either facilitator's high costs or complexity of modelled relationships that cannot be grasped by humans. This paper provides a facilitator-free approach based on an advanced knowledgesharing methodology. It presents the approach on commonly available types of knowledge and applies the methodology to a normal controlled autoregressive model.

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Prior information in structure estimation

Cited by 12 publications

References 5 publications

Prior knowledge processing for initial state of Kalman filter

Prior knowledge processing for initial state of Kalman filter

Use of Kullback–Leibler divergence for forgetting

Fully probabilistic knowledge expression and incorporation

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