Talk:Extrapolation

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Mathematics Mid‑priority

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Statistics High‑importance

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Removing statistics content

I am removing the sentence ..."The extent to which an extrapolation is accurate is known as the "prediction confidence interval", and is usually expressed as an upper and lower boundary within which the prediction is expected to be accurate 19 times out of 20 (a 95% confidence interval)." ... on the grounds that while this might be possible it requires a large set of context and assumptions which are not stated. Also removing from Category:Statistics for now. Of course there is the possibility of including some properly contextualised statistical content. Melcombe (talk) 15:52, 13 May 2008 (UTC)[reply]

extrapolation - literature

I don't know if this is the correct section to write a comment? I was just wondering that the entry for "extrapolation" doesn't mention the literary aspect at all. It's a quite common method in science fiction or utopian/dystopian literature. —Preceding unsigned comment added by Moonlight1981 (talk • contribs) 19:45, 15 December 2008 (UTC)[reply]

French curve extrapolation

A missing link (the site http://www.aidscjduk.info/ is down and seems do have been so for some time) aroused my curiosity. I could not find any mention of this technique outside of this article (and copies thereof) and cannot remember anything like it from my own numerics lecture. As the primary source is missing, no secondary sources can be found, and the section does not actually explain anything about the technique, I suggest removing this section. 134.93.136.193 (talk) 14:26, 9 April 2013 (UTC)[reply]

Rational extrapolation

A suspected or known asymptotic behavior may be imposed on the extrapolating function, as the only term which does not tend to zero. When the asymptotic behavior is polynomial in nature, one can model the function using a rational function such that the desired asymptotic behavior is achieved while still matching the specified points. Compared to polynomial extrapolation, rational functions offer the following trade-offs: (1) Rational functions can model a larger variety of functions, (2) rational functions may have poles (zeros of the denominator), (3) only when all poles are imaginary, then the intermediate value theorem applies, (4) with a numerator of degree n and a denominator of degree d, when n>=d, then the asymptotic behavior will be that of an (n-d) polynomial, (5) it is more work to determine the coefficients.

For example, say a researcher has some data and knows that the asymptotic behavior must be linear. A linear equation may fit the data poorly and generalize (extrapolate) poorly as well especially when the data exhibits cusps or any nonlinearity. A rational function with a numerator of degree three and a denominator of degree two will have the linear asymptotic behavior while also being able to model the nonlinearities. The main drawback is that the total degrees of freedom may need to be constrained to avoid overfitting the data. The simple linear equation, $ax+b$ , has two degrees of freedom. A rational function of the form, ${\frac {x^{3}}{a*x^{2}+b}},b>0$ , would also have two degrees of freedom and only imaginary poles.