Likelihood Based Uncertainty Bounding in Prediction Error - PowerPoint PPT Presentation

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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 July 4, 2007 1 Delft Center for Systems and Control

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
Confidence regions • 1 0.95 0.9 0.85 0.8 0.75 b 0.7 0.65 0.6 0.55 0.5 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 a July 4, 2007 2 Delft Center for Systems and Control
Outline July 4, 2007 3 Delft Center for Systems and Control
Data generating system and predictor model July 4, 2007 4 Delft Center for Systems and Control
Statistical inference July 4, 2007 5 Delft Center for Systems and Control
Statistical inference 1 0.95 0.9 0.85 0.8 b 0.75 0.7 0.65 0.6 0.55 0.5 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 a July 4, 2007 6 Delft Center for Systems and Control
Construction of confidence regions 1 0.95 0.9 0.85 0.8 0.75 b 0.7 0.65 0.6 0.55 0.5 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 a July 4, 2007 7 Delft Center for Systems and Control
Test statistics July 4, 2007 8 Delft Center for Systems and Control
ARX modelling July 4, 2007 9 Delft Center for Systems and Control
Confidence regions for ARX parameters July 4, 2007 10 Delft Center for Systems and Control
Result from asymptotic theory ( θ 0 known) July 4, 2007 11 Delft Center for Systems and Control
Simulation experiment July 4, 2007 12 Delft Center for Systems and Control
observed coverage rates 1 0.95 0.9 0.85 0.8 0.75 0.7 0.65 0.6 0.55 0.5 0.45 0 50 100 150 200 250 300 350 400 number of data points N July 4, 2007 13 Delft Center for Systems and Control
observed coverage rates 1 0.95 0.9 0.85 0.8 0.75 0.7 0.65 0.6 0.55 0.5 0.45 0.4 0.35 0.3 0 50 100 150 200 250 300 350 400 number of data points N July 4, 2007 14 Delft Center for Systems and Control
Conclusions July 4, 2007 15 Delft Center for Systems and Control
ARX modelling July 4, 2007 16 Delft Center for Systems and Control
Result from asymptotic theory ( θ 0 known) July 4, 2007 17 Delft Center for Systems and Control

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