|WikiProject Statistics||(Rated Start-class, Mid-importance)|
I can try to edit this page soon, perhaps tomorrow. Plf515 03:29, 24 November 2006 (UTC)plf515
Merging Smoothing with Curve fitting?
- Care to elaborate? Perhaps give an example of one that is not also an example of the other? Btyner (talk) 23:53, 1 May 2008 (UTC)
- I have added a little to attempt to distinguish smoothing from curve fitting. Melcombe (talk) 12:43, 20 May 2008 (UTC)
Why does someone insist on linking interpolating splines to this page? Interpolation is in no way "leaving out noise" (cf. paragraph 1). Unless the claim that an interpolation spline "is sometimes called smoothing" can be backed up by a credible reference, interpolation shouldn't be mentioned here.
Smoothing vs Curve Fitting
Also, can someone rewrite the paragraphs comparing smoothing and curve fitting? What's presently there is just nonsensical. Curve fitting, as it's defined on wikipedia, is an umbrella term that covers interpolation, regression, smoothing and a whole host of other things. Failing a rewrite, everything except the first paragraph of the introduction should just be deleted (which would be my preference). --Zaqrfv (talk) 10:08, 3 September 2008 (UTC)
- A brief reply. While it is true that curve fitting can be used for some types of smoothing, the terminology of curve fitting does not encompass all types of smoothing, for example not the way the term "smoothing" is used in image processing and computer vision. Hence, the notion of curve fitting cannot be regarded as an "umbrella term" for smoothing. Tpl (talk) 10:46, 3 September 2008 (UTC)
- Ok, I'm talking as a statistician, so mean statistical smoothing. What would be much more useful than the present introduction would be separate one-paragraph summaries of smoothing in each main area of application (statistics, image processing, ...). From that base, the rest of the article could expand methods, and highlight similarities and differences of "smoothing" in different fields. --Zaqrfv (talk) 11:22, 3 September 2008 (UTC)
Smoothing in computational solvers
Smoothing goes far beyond data manipulation and signal processing. It is a major concept in computational solvers and numerical analysis and an inherent by-product of (simulated) Diffusion (but only casually mentioned in the Numerical diffusion article). Stationary iterative methods are also dubbed "smoothers" since they (iteratively) reduce the solution's error in the discrete domain by smoothing or averaging it out. These iterative smoothing methods are also an important part in the Multigrid method.
It might also be worth mentioning the fact that iterative "smoothing" and (simulated) "diffusion" are very similar: They eliminate high frequencies first and low frequencies are eliminated after many iterations/after a long time. In fact, infinite frequencies are eliminated instantly, which is why a vector field, only subject to diffusion, never has discontinuities.
Since my explanations are lacking rigor, I am hoping that someone with more insight can help out on this topic.
One other thing: Gilbert Strang often talks about "smoothing" (in the context of Elliptic solvers) in his course "Mathematical Methods for Engineers II".
18.104.22.168 (talk) 19:12, 23 January 2013 (UTC)
The Smoothing problem is not convolution Smoothing. Avoid confusion.
The smoothing and Smoothing problem (stochastic processes) are totally different topics with the same name. They should be separated into separate articles to avoid confusion. I suggest "smoothing" versus "smoothing problem" (or even better, "smoother"; however the filter dual cannot be called "filterer"). Please see articles Smoothing problem (stochastic processes) and Filtering problem (stochastic processes).
Smoothing can mean totally different (but sound like an apparently similar) concepts and are used in different historical contexts. They are problems with very different requirements.
1. The smoothing in the sense of convolution (eg, moving average, low-pass filtering, convolution with a kernel, or blurring using Laplace filters in image processing) is simpler. Especially non-stochastic and non-Bayesian signal processing, without hidden variables.
2. The smoothing problem uses Bayesian and state-space models to model hidden state variables. This is used in the context of World War 2 defined by people like Norbert Wiener, in (stochastic) control theory, radar, signal detection, tracking, etc. The most common use is the Kalman Smoother used with Kalman Filter, which is actually developed by Rauch. The procedure is called Kalman-Rauch recursion. It is one of the main problems defined by Norbert Wiener  .
Most importantly, in the Filtering problem the information from observation up to the time of the current sample is used. In smoothing all observation samples are used (from future). Filtering is causal but smoothing is batch processing of the same problem, namely, estimation of a time-series process based on serial incremental observations.
Please see Smoothing problem (stochastic processes)#Relation_between_Filtering_and_Smoothing_problems for more information.
I also suggest a separate article for the "pair problems", the smoothing problem and filtering problem in the sense defined by Wiener (see above link). But each deserves their articles. — Preceding unsigned comment added by Sohale (talk • contribs) 16:13, 20 March 2017 (UTC)
- 1942, Extrapolation, Interpolation and Smoothing of Stationary Time Series. A war-time classified report nicknamed "the yellow peril" because of the color of the cover and the difficulty of the subject. Published postwar 1949 MIT Press. http://www.isss.org/lumwiener.htm])
- Wiener, Norbert (1949). Extrapolation, Interpolation, and Smoothing of Stationary Time Series. New York: Wiley. ISBN 0-262-73005-7.