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Error propagation: Difference between revisions
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The presence of collinearity may affect error levels enormously. | The presence of collinearity may affect error levels enormously. | ||
A quick check of possible problems in this sense can be made using the [[:Wikipedia:Monte Carlo method|Monte Carlo approach]] (see below). | A quick check of possible problems in this sense can be made using the [[:Wikipedia:Monte Carlo method|Monte Carlo approach]] (see below). | ||
Several techniques are available to handle collinearity, such as Principal | Several techniques are available to handle collinearity, such as [[:Wikipedia:Principal component analysis|Principal component analysis]] (basically, by orthogonalization of the correlation matrix of ''s''). | ||
The Monte Carlo approach also provides a simple method for error estimation for the much more difficult problem of a non-linear mapping ''M<sub>p</sub>''. | The Monte Carlo approach also provides a simple method for error estimation for the much more difficult problem of a non-linear mapping ''M<sub>p</sub>''. | ||
This technique proceeds as follows. | This technique proceeds as follows. | ||
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When the model relating ''s'' and ''p'' is known, as well as the error distributions (and the latter may either be Gaussian or not), a more systematic approach to error propagation is provided by a technique known as the [[:Wikipedia:Maximum likelihood|maximum likelihood method]]. | When the model relating ''s'' and ''p'' is known, as well as the error distributions (and the latter may either be Gaussian or not), a more systematic approach to error propagation is provided by a technique known as the [[:Wikipedia:Maximum likelihood|maximum likelihood method]]. | ||
<ref>Particle Data Group, Eur. Phys. J. C 3, 1 (1998)</ref> | <ref>Particle Data Group, Eur. Phys. J. C 3, 1 (1998)</ref> | ||
This technique is simply the generalisation of standard error propagation to general error distributions (i.e. not limited to Gaussians). | This technique is simply the generalisation of standard error propagation to general error distributions (i.e. not limited to Gaussians). | ||
== Systematic and random errors == | == Systematic and random errors == | ||