Model error
A model error results from an incorrect model approach. Such an error is not a statistical phenomenon, but a so-called reality phenomenon and can therefore be corrected, for example, by correcting the model structure.
In principle, it is not possible to create an error-free model, any more than it would be possible to carry out an error-free measurement. A model is used to visualize a reality, i.e. a view of an object or a process, for example. Such a view is limited by the selected viewing angle (aspect) or the period of observation and reflects a selection or a simplification. The model relation is therefore never continuously isomorphic (reversibly unique).
The arbitrary information reduction associated with each model always leads to a restriction of the validity of the model and can ultimately lead to completely wrong conclusions from the model.
Demarcation
A model error is therefore not covered by the definition of the standard DIN 1319-1: 1995, Fundamentals of Measurement Technology - Part 1: Basic Terms, which describes an error as a numerical phenomenon: "The variable to be measured is not correctly recorded due to a large number of causes ". The deviation of a value obtained from measurements from the true value of the measured variable is called measurement deviation (according to DIN 1319-1: 1995) or measurement error (old name).
According to the given source, there are generally at least four classes of errors:
- Model errors that arise because the mathematical model used describes the reality phenomenon to be examined in a simplified manner
- Data errors that arise from random measurement errors and technical measurement inaccuracies
- Procedural errors that arise when the mathematical model is replaced by a constrained numerical approximation
- Rounding errors that arise because the processing of the measured values only calculates with a fixed number of digits.
Further errors arise because the intentions of the modeler do not lead to the mentioned restrictions due to a lack of qualification, but also choose a wrong approach, which for example:
- stochastic independence of measured variables assumed, although there is a systematic relationship ,
- a sufficient representation of a measurement series or sample is assumed, although the scope of the survey or recording is insufficient
- omits a time-bound trend because it simplifies the model considerably
- suppresses any information quality because it is not recognized
- pursues a certain objective and for this purpose shortens the modeling of reality.
In a similar way, the intentions of the modeler can be falsified in that a criticism of the modeling connects further views to the model that the model does not, cannot yet, or will never detect by
- a certain perception is assumed to be mandatory without this perception being included in the model.
- a certain norm is applied without this norm being temporal, causal or modal.
There is no limit to the quality and quantity of these lists.
Hermeneutics
Philosophy and systems theory deal, for example, with the hermeneutics of model errors or conceptual errors:
- A conceptual flaw occurs when an incorrect model is used to describe a system. Systems engineering or other model theories provide methods for handling conceptual errors .
Example: A typical example is time-invariant modeling for a time-variant variable. This approach is often chosen with knowledge of the conceptual defect, if there is no adequate representation for the time variation.
- A systematic error arises when reality is represented by an inadequate mathematical model.
Example: A typical example is the description of a monotonically increasing quantity using a bell curve . This approach is often used as long as there is no qualified test of the chosen statistical hypothesis.
See also
Individual evidence
- ↑ a b Trottenberg, Numerik, Chapter 2 ( Memento of the original from July 26, 2014 in the Internet Archive ) Info: The archive link was inserted automatically and has not yet been checked. Please check the original and archive link according to the instructions and then remove this notice. (PDF; 276 kB).
- ↑ http://www.din.de/cmd?level=tpl-home&contextid=din Basics of measurement technology.
