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2.160 Identification, Estimation, and Learning (MIT) 2.160 Identification, Estimation, and Learning (MIT)

Description

This course provides a broad theoretical basis for system identification, estimation, and learning. Students will study least squares estimation and its convergence properties, Kalman filters, noise dynamics and system representation, function approximation theory, neural nets, radial basis functions, wavelets, Volterra expansions, informative data sets, persistent excitation, asymptotic variance, central limit theorems, model structure selection, system order estimate, maximum likelihood, unbiased estimates, Cramer-Rao lower bound, Kullback-Leibler information distance, Akaike's information criterion, experiment design, and model validation. This course provides a broad theoretical basis for system identification, estimation, and learning. Students will study least squares estimation and its convergence properties, Kalman filters, noise dynamics and system representation, function approximation theory, neural nets, radial basis functions, wavelets, Volterra expansions, informative data sets, persistent excitation, asymptotic variance, central limit theorems, model structure selection, system order estimate, maximum likelihood, unbiased estimates, Cramer-Rao lower bound, Kullback-Leibler information distance, Akaike's information criterion, experiment design, and model validation.

Subjects

system identification; estimation; least squares estimation; Kalman filter; noise dynamics; system representation; function approximation theory; neural nets; radial basis functions; wavelets; volterra expansions; informative data sets; persistent excitation; asymptotic variance; central limit theorem; model structure selection; system order estimate; maximum likelihood; unbiased estimates; Cramer-Rao lower bound; Kullback-Leibler information distance; Akaike?s information criterion; experiment design; model validation. | system identification; estimation; least squares estimation; Kalman filter; noise dynamics; system representation; function approximation theory; neural nets; radial basis functions; wavelets; volterra expansions; informative data sets; persistent excitation; asymptotic variance; central limit theorem; model structure selection; system order estimate; maximum likelihood; unbiased estimates; Cramer-Rao lower bound; Kullback-Leibler information distance; Akaike?s information criterion; experiment design; model validation. | system identification | system identification | estimation | estimation | least squares estimation | least squares estimation | Kalman filter | Kalman filter | noise dynamics | noise dynamics | system representation | system representation | function approximation theory | function approximation theory | neural nets | neural nets | radial basis functions | radial basis functions | wavelets | wavelets | volterra expansions | volterra expansions | informative data sets | informative data sets | persistent excitation | persistent excitation | asymptotic variance | asymptotic variance | central limit theorem | central limit theorem | model structure selection | model structure selection | system order estimate | system order estimate | maximum likelihood | maximum likelihood | unbiased estimates | unbiased estimates | Cramer-Rao lower bound | Cramer-Rao lower bound | Kullback-Leibler information distance | Kullback-Leibler information distance | Akaike?s information criterion | Akaike?s information criterion | experiment design | experiment design | model validation | model validation

License

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see http://ocw.mit.edu/terms/index.htm

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12.990 Prediction and Predictability in the Atmosphere and Oceans (MIT) 12.990 Prediction and Predictability in the Atmosphere and Oceans (MIT)

Description

Forecasting is the ultimate form of model validation. But even if a perfect model is in hand, imperfect forecasts are likely. This course will cover the factors that limit our ability to produce good forecasts, will show how the quality of forecasts can be gauged a priori (predicting our ability to predict!), and will cover the state of the art in operational atmosphere and ocean forecasting systems. Forecasting is the ultimate form of model validation. But even if a perfect model is in hand, imperfect forecasts are likely. This course will cover the factors that limit our ability to produce good forecasts, will show how the quality of forecasts can be gauged a priori (predicting our ability to predict!), and will cover the state of the art in operational atmosphere and ocean forecasting systems.

Subjects

Forecasting | Forecasting | model validation | model validation | prediction quality | prediction quality | operational atmosphere and ocean forecasting systems | operational atmosphere and ocean forecasting systems | limiting factors | limiting factors | prediction | prediction | operational atmosphere forecasting systems | operational atmosphere forecasting systems | ocean forecasting systems | ocean forecasting systems | chaos | chaos | probabilistic forecasting | probabilistic forecasting | data assimilation | data assimilation | adaptive observations | adaptive observations | model error | model error | attractors | attractors | dimensions | dimensions | sensitive dependence | sensitive dependence | initial conditions | initial conditions

License

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see http://ocw.mit.edu/terms/index.htm

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2.160 Identification, Estimation, and Learning (MIT)

Description

This course provides a broad theoretical basis for system identification, estimation, and learning. Students will study least squares estimation and its convergence properties, Kalman filters, noise dynamics and system representation, function approximation theory, neural nets, radial basis functions, wavelets, Volterra expansions, informative data sets, persistent excitation, asymptotic variance, central limit theorems, model structure selection, system order estimate, maximum likelihood, unbiased estimates, Cramer-Rao lower bound, Kullback-Leibler information distance, Akaike's information criterion, experiment design, and model validation.

Subjects

system identification; estimation; least squares estimation; Kalman filter; noise dynamics; system representation; function approximation theory; neural nets; radial basis functions; wavelets; volterra expansions; informative data sets; persistent excitation; asymptotic variance; central limit theorem; model structure selection; system order estimate; maximum likelihood; unbiased estimates; Cramer-Rao lower bound; Kullback-Leibler information distance; Akaike?s information criterion; experiment design; model validation. | system identification | estimation | least squares estimation | Kalman filter | noise dynamics | system representation | function approximation theory | neural nets | radial basis functions | wavelets | volterra expansions | informative data sets | persistent excitation | asymptotic variance | central limit theorem | model structure selection | system order estimate | maximum likelihood | unbiased estimates | Cramer-Rao lower bound | Kullback-Leibler information distance | Akaike?s information criterion | experiment design | model validation

License

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see https://ocw.mit.edu/terms/index.htm

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12.990 Prediction and Predictability in the Atmosphere and Oceans (MIT)

Description

Forecasting is the ultimate form of model validation. But even if a perfect model is in hand, imperfect forecasts are likely. This course will cover the factors that limit our ability to produce good forecasts, will show how the quality of forecasts can be gauged a priori (predicting our ability to predict!), and will cover the state of the art in operational atmosphere and ocean forecasting systems.

Subjects

Forecasting | model validation | prediction quality | operational atmosphere and ocean forecasting systems | limiting factors | prediction | operational atmosphere forecasting systems | ocean forecasting systems | chaos | probabilistic forecasting | data assimilation | adaptive observations | model error | attractors | dimensions | sensitive dependence | initial conditions

License

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see https://ocw.mit.edu/terms/index.htm

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