Mathematical data production model with limited structure
In mathematics, statistics, and computational modelling, a grey box model[1][2][3][4] combines a partial theoretical structure with data to complete the model. The theoretical structure may vary from information on the smoothness of results, to models that need only parameter values from data or existing literature.[5] Thus, almost all models are grey box models as opposed to black box where no model form is assumed or white box models that are purely theoretical. Some models assume a special form such as a linear regression[6][7] or neural network.[8][9] These have special analysis methods. In particular linear regression techniques[10] are much more efficient than most non-linear techniques.[11][12] The model can be deterministic or stochastic (i.e. containing random components) depending on its planned use.
^Bohlin, Torsten P. (7 September 2006). Practical Grey-box Process Identification: Theory and Applications. Springer Science & Business Media. ISBN 978-1-84628-403-8.
^"Grey-box model estimation". Mathworks 2. 2012.
^Kroll, Andreas (2000). Grey-box models: Concepts and application. In: New Frontiers in Computational Intelligence and its Applications, vol.57 of Frontiers in artificial intelligence and applications, pp. 42-51. IOS Press, Amsterdam.
^Sohlberg, B., and Jacobsen, E.W., 2008. Grey box modelling - branches and experiences, Proc. 17th World Congress, Int. Federation of Automatic Control, Seoul. pp 11415-11420
^Whiten, B., 2013. Model completion and validation using inversion of grey box models, ANZIAM J.,54 (CTAC 2012) pp C187–C199.
^Draper, Norman R.; Smith, Harry (25 August 2014). Applied Regression Analysis. John Wiley & Sons. pp. 657–. ISBN 978-1-118-62568-2.
^Weisberg, Sanford (25 November 2013). Applied Linear Regression. Wiley. ISBN 978-1-118-59485-8.
^Heaton, J., 2012. Introduction to the math of neural networks, Heaton Research Inc. (Chesterfield, MO), ISBN 978-1475190878
^Stergiou, C.; Siganos, D. (2013). "Neural networks". Archived from the original on 2009-12-16. Retrieved 2013-07-03.
^Lawson, Charles L.; J. Hanson, Richard (1 December 1995). Solving Least Squares Problems. SIAM. ISBN 978-0-89871-356-5.
^Press, W.H.; Teukolsky, S.A.; Vetterling, W.T.; Flannery, B.P. (2007). Numerical Recipes (3rd ed.). Cambridge University Press. ISBN 978-0-521-88068-8.
^Gelman, Andrew; Carlin, John B.; Stern, Hal S.; Dunson, David B.; Vehtari, Aki; Rubin, Donald B. (1 November 2013). Bayesian Data Analysis, Third Edition. CRC Press. ISBN 978-1-4398-4095-5.
statistics, and computational modelling, a greyboxmodel combines a partial theoretical structure with data to complete the model. The theoretical structure...
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The New York Times. ISSN 0362-4331. Retrieved 2020-05-22. "The Grey Zone (2002)". Box Office Mojo. Retrieved July 6, 2011. Holden, Stephen (2002-10-18)...
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observed dynamics are present in the model structure. The resulting models are not black box, but are greyboxmodels that have parameters and structure...