On the problem of ambiguities in maximum likelihood identification

Bohlin, Torsten

doi:10.1016/0005-1098(71)90063-x

Cited by 86 publications

(24 citation statements)

References 8 publications

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“…In classical linear model identification, correlation function-based model validation tests have been widely applied to validate the estimated models (Bohlin 1971;Box and Jenkins 1976;So¨derstro¨m and Stoica 1990). Model validation tests are procedures to detect the inadequacy of the model.…”

Section: Correlation-based Model Validationmentioning

confidence: 99%

Model selection approaches for non-linear system identification: a review

Hong

Mitchell

Chen

et al. 2008

International Journal of Systems Science

203

142

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Section: Correlation-based Model Validationmentioning

confidence: 99%

Model selection approaches for non-linear system identification: a review

Hong

Mitchell

Chen

et al. 2008

International Journal of Systems Science

203

142

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“…To provide better solutions, ACF-and CCF-based linear model validation methods have been proposed to check if the residuals are correlated to delayed residuals, inputs, and outputs [6]- [9]. For nonlinear model validation, ACF and CCF are obviously insufficient since nonlinear terms may exist in residuals.…”

Section: Correlation-test-based Neural Network Validationmentioning

confidence: 99%

“…For linear model validation, autocorrelation function (ACF) and cross-correlation function (CCF) have been successfully applied to detect the whiteness and randomness of the residuals [6]- [9]. For nonlinear model validation, several higher order correlation-test-based approaches have been developed for detecting the nonlinear correlationships between residuals and delayed residuals, inputs and outputs [10]- [16].…”

Section: Introductionmentioning

confidence: 99%

A Correlation-Test-Based Validation Procedure for Identified Neural Networks

Zhang

Zhu

Longden

2009

IEEE Trans. Neural Netw.

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We recommend you cite the published version. The publisher's URL is http://dx.doi.org/10.1109/ TNN.2008.2003223 Refereed: Yes (c) 2009 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other users, including reprinting/ republishing this material for advertising or promotional purposes, creating new collective works for resale or redistribution to servers or lists, or reuse of any copyrighted components of this work in other works. DisclaimerUWE has obtained warranties from all depositors as to their title in the material deposited and as to their right to deposit such material. UWE makes no representation or warranties of commercial utility, title, or fitness for a particular purpose or any other warranty, express or implied in respect of any material deposited.UWE makes no representation that the use of the materials will not infringe any patent, copyright, trademark or other property or proprietary rights.UWE accepts no liability for any infringement of intellectual property rights in any material deposited but will remove such material from public view pending investigation in the event of an allegation of any such infringement. PLEASE SCROLL DOWN FOR TEXT. I. INTRODUCTIONN EURAL NETWORK (NN) has been extensively studied and applied as a generic and powerful black-box modeling technique to enhance complex nonlinear system modeling and identification [1]- [4]. In system identification procedure, validation is the final step to check the adequacy of identified models. Because an NN could be incorrectly designed due to many problems such as incorrect network selection, incorrect input vector selection, insufficient training, and overfitting, validation is a very important means to determine if the NN agrees sufficiently well with the observations. Generally, the basic statistics of residuals, e.g., mean and variance or standard deviation, are considered to be critical indices for the identified NNs to check whether the residuals are reduced to the lowest possible levels. However, the levels of the residuals sometimes cannot clearly and directly indicate the adequacy of the identified NNs since the original systems are always contaminated in unknown noisy environments.To properly validate linear and nonlinear models, several methods for model validation based on correlation tests have been developed that are based on the concept that if a model is valid, the residuals should be reduced to a white noise and uncorrelated to the delayed system inputs and outputs [5]. Manuscript received September 21, 2006; revised August 23, 2007 and April 04, 2008; accepted April 16, 2008 . In comparison to previous higher order correlation-test-based approaches, the new method provides an enhanced nonlinear correlation detection power and a condensed correlation illustration. It should be mentioned that almost all previous validity tests only focus on the correlation computation for residuals and inputs. In these methods, the correlation between residuals and delayed outputs is i...

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“…The CML model (5-9) was simulated with the parameters set above for 100 steps over the 50 50 × lattice 2 I starting from a randomly generated initial population and periodic boundary conditions. Snapshots of the spatiotemporal patterns at different times are shown in Figure (5-3) ε is random and correlated with the nonlinear terms defined in Equation (5-13) and Equation (5)(6)(7)(8)(9)(10)(11)(12)(13)(14).…”

Section: Example 2 -A Nonlinear Spatiotemporal System Described By a mentioning

confidence: 99%

“…If the model structure is correct and the estimated parameters are unbiased, the model residuals or the one-step-ahead prediction errors should be a random time sequence with zero mean and finite variance. The auto-correlation function (ACF) and the cross-correlation function (CCF) have been widely used in linear temporal model validation (Bohlin, 1971, 1978, Soderstrom and Stoica, 1990. It is well known that the ACF of the residuals and the CCF between the residuals and input should fall within preset confidence intervals if the identified model is correct and the residual sequence is white.…”

Section: Introductionmentioning

confidence: 99%

Model Validation of Spatiotemporal Systems Using Correlation Function Tests

Pan

Billings

2007

Int. J. Bifurcation Chaos

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Model validation is an important and essential final step in system identification. Although model validation for nonlinear temporal systems has been extensively studied, model validation for spatiotemporal systems is still an open question. In this paper, correlation based methods, which have been successfully applied in nonlinear temporal systems are extended and enhanced to validate models of spatiotemporal systems.Examples are included to demonstrate the application of the tests.

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On the problem of ambiguities in maximum likelihood identification

Cited by 86 publications

References 8 publications

Model selection approaches for non-linear system identification: a review

Model selection approaches for non-linear system identification: a review

A Correlation-Test-Based Validation Procedure for Identified Neural Networks

Model Validation of Spatiotemporal Systems Using Correlation Function Tests

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