Error analysis in numerical modeling
In numerical analysis, error analysis comprises both forward error analysis and backward error analysis. Forward error analysis involves the analysis of a function which is an approximation (usually a finite polynomial) to a function to determine the bounds on the error in the approximation; i.e., to find such that . Backward error analysis involves the analysis of the approximation function , to determine the bounds on the parameters such that the result .
Error analysis in second language acquisition
- modality (i.e., level of proficiency in speaking, writing, reading, listening)
- linguistic levels (i.e., pronunciation, grammar, vocabulary, style)
- form (e.g., omission, insertion, substitution)
- type (systematic errors/errors in competence vs. occasional errors/errors in performance)
- cause (e.g., interference, interlanguage)
- norm vs. system
Error analysis in SLA was established in the 1960s by Stephen Pit Corder and colleagues. Error analysis was an alternative to contrastive analysis, an approach influenced by behaviorism through which applied linguists sought to use the formal distinctions between the learners' first and second languages to predict errors. Error analysis showed that contrastive analysis was unable to predict a great majority of errors, although its more valuable aspects have been incorporated into the study of language transfer. A key finding of error analysis has been that many learner errors are produced by learners making faulty inferences about the rules of the new language.
Error analysis in molecular dynamics simulation
In molecular dynamics (MD) simulations, there are errors due to inadequate sampling of the phase space or infrequently occurring events, these lead to the statistical error due to random fluctuation in the measurements.
For a series of M measurements of a fluctuating property A, the mean value is:
When these M measurements are independent, the variance of the mean <A> is:
but in most MD simulations, there is correlation between quantity A at different time, so the variance of the mean <A> will be underestimated as the effective number of independent measurements is actually less than M. In such situations we rewrite the variance as :
where is the autocorrelation function defined by
- Error analysis (linguistics)
- Error bar
- Errors and residuals in statistics
- Propagation of uncertainty
- James W. Haefner (1996). Modeling Biological Systems: Principles and Applications. Springer. pp. 186–189. ISBN 0412042010.
- Francis J. Scheid (1988). Schaum's Outline of Theory and Problems of Numerical Analysis. McGraw-Hill Professional. p. 11. ISBN 0070552215.
- Cf. Bussmann, Hadumod (1996), Routledge Dictionary of Language and Linguistics, London: Routledge, s.v. error analysis. A comprehensive bibliography was published by Bernd Spillner (1991), Error Analysis, Amsterdam/Philadelphia: Benjamins.
- Corder, S. P. (1967). "The significance of learners' errors". International Review of Applied Linguistics 5: 160–170. doi:10.1515/iral.1967.5.1-4.161.
- D. C. Rapaport, The Art of Molecular Dynamics Simulation, Cambridge University Press.
-  All about error analysis.