Modeling Error
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measure its prediction error is of key importance. Often, however, techniques of measuring error are used that give grossly misleading results. This can lead to the phenomenon of over-fitting where a model may fit the training data very well, but will do a poor job of predicting results for new data not used in model errors in variables model training. Here is an overview of methods to accurately measure model prediction error. Measuring Error When building
Measurement Error In Dependent Variable
prediction models, the primary goal should be to make a model that most accurately predicts the desired target value for new data. The measure of model
Modeling Error Definition
error that is used should be one that achieves this goal. In practice, however, many modelers instead report a measure of model error that is based not on the error for new data but instead on the error the very same data
Error In Variables Regression In R
that was used to train the model. The use of this incorrect error measure can lead to the selection of an inferior and inaccurate model. Naturally, any model is highly optimized for the data it was trained on. The expected error the model exhibits on new data will always be higher than that it exhibits on the training data. As example, we could go out and sample 100 people and create a regression model to predict an individual's happiness based on their wealth. We can model error statistics record the squared error for how well our model does on this training set of a hundred people. If we then sampled a different 100 people from the population and applied our model to this new group of people, the squared error will almost always be higher in this second case. It is helpful to illustrate this fact with an equation. We can develop a relationship between how well a model predicts on new data (its true prediction error and the thing we really care about) and how well it predicts on the training data (which is what many modelers in fact measure). $$ True\ Prediction\ Error = Training\ Error + Training\ Optimism $$ Here, Training Optimism is basically a measure of how much worse our model does on new data compared to the training data. The more optimistic we are, the better our training error will be compared to what the true error is and the worse our training error will be as an approximation of the true error. The Danger of Overfitting In general, we would like to be able to make the claim that the optimism is constant for a given training set. If this were true, we could make the argument that the model that minimizes training error, will also be the model that will minimize the true prediction error for new data. As a consequence, even though our reported training error might be a bit optimistic, using it to compare models will cause us to still select the
ChapterGreen's Functions and Finite Elements pp 241-317 Date: 01 August 2012Modeling ErrorFriedel HartmannAffiliated withStructural Mechanics, University of Kassel Email author Buy this eBook * Final gross prices may modelling error in numerical methods vary according to local VAT. Get Access Abstract How do modeling errors influence attenuation bias proof the output values? How do displacements or stresses change if the coefficients of the differential equation change? Any change in measurement error bias definition the underlying equation translates into a change of the stiffness matrix and its inverse. We apply a 'direct' method to calculate the solution vector of the modified system. In this approach it http://scott.fortmann-roe.com/docs/MeasuringError.html is not the stiffness matrix which gets modified but the right-hand side. This allows to operate on the modified system with the Green's functions of the original system. Each entry of the inverse of the stiffness matrix changes if one coefficient of the stiffness matrix changes and so and so such a change requires a complete reanalysis. In an alternative formulation integration needs only to http://link.springer.com/chapter/10.1007%2F978-3-642-29523-2_5 be done over the defective element. This integral is the strain energy product between the Green's function and the modified solution. It is a weak influence function. Various techniques are discussed how best to calculate this form in the context of the FE-method. By solving small auxiliary problems the effects caused by changes in an element stiffness can be calculated exactly. Page %P Close Plain text Look Inside Chapter Metrics Provided by Bookmetrix Reference tools Export citation EndNote (.ENW) JabRef (.BIB) Mendeley (.BIB) Papers (.RIS) Zotero (.RIS) BibTeX (.BIB) Add to Papers Other actions About this Book Reprints and Permissions Share Share this content on Facebook Share this content on Twitter Share this content on LinkedIn Supplementary Material (0) References (6) References1.Novartis Pharma AG Campus, Structural Engineers: Schlaich Bergermann and Partner, Software: SOFiSTiK2.Deif A (1986) Sensitivity analysis in linear systems. Springer, Berlin3.Choi KK, Kim NH (2005) Structural sensitivity analysis and optimization 1—linear systems. Springer, Berlin4.Choi KK, Kim NH (2005) Structural sensitivity analysis and optimization 2—nonlinear systems and applications. Springer, Berlin5.Strang G (2007) Computational science and engineering. Wellesley-Cambridge Press, Wellesley6.Nikulla S (2012) Quality assesment of kinematical models by means of global and goal-oriented error esti
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