Likelihood Based Uncertainty Bounding in Prediction Error - - PowerPoint PPT Presentation

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likelihood based uncertainty bounding in prediction error

Likelihood Based Uncertainty Bounding in Prediction Error - - PowerPoint PPT Presentation

Oct 03, 2023 336 likes •518 views

Likelihood Based Uncertainty Bounding in Prediction Error Identification using ARX models A Simulation Study ECC 2007, Kos, Greece Arjan den Dekker, Xavier Bombois and Paul Van den Hof July 4, 2007 1 Delft Center for Systems and Control

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July 4, 2007

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Likelihood Based Uncertainty Bounding in Prediction Error Identification using ARX models

A Simulation Study

ECC 2007, Kos, Greece Arjan den Dekker, Xavier Bombois and Paul Van den Hof

Delft Center for Systems and Control

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July 4, 2007 2

Confidence regions

0.05

0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 0.5 0.55 0.6 0.65 0.7 0.75 0.8 0.85 0.9 0.95 1 a b

Delft Center for Systems and Control

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July 4, 2007 3

Outline

Delft Center for Systems and Control

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July 4, 2007 4

Data generating system and predictor model

Delft Center for Systems and Control

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July 4, 2007 5

Statistical inference

Delft Center for Systems and Control

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Statistical inference

0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 0.5 0.55 0.6 0.65 0.7 0.75 0.8 0.85 0.9 0.95 1 a b

Delft Center for Systems and Control

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Construction of confidence regions

0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 0.5 0.55 0.6 0.65 0.7 0.75 0.8 0.85 0.9 0.95 1 a b

Delft Center for Systems and Control

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Test statistics

Delft Center for Systems and Control

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ARX modelling

Delft Center for Systems and Control

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Confidence regions for ARX parameters

Delft Center for Systems and Control

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Result from asymptotic theory (θ0 known)

Delft Center for Systems and Control

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Simulation experiment

Delft Center for Systems and Control

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50 100 150 200 250 300 350 400 0.45 0.5 0.55 0.6 0.65 0.7 0.75 0.8 0.85 0.9 0.95 1 number of data points N

bserved coverage rates

Delft Center for Systems and Control

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50 100 150 200 250 300 350 400 0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7 0.75 0.8 0.85 0.9 0.95 1 number of data points N

bserved coverage rates

Delft Center for Systems and Control

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Conclusions

Delft Center for Systems and Control

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ARX modelling

Delft Center for Systems and Control

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Result from asymptotic theory (θ0 known)

Delft Center for Systems and Control