Alpha beta filter: Difference between revisions

From formulasearchengine
Jump to navigation Jump to search
← Older editNewer edit →
en>BG19bot
m →‎The alpha beta gamma extension: WP:CHECKWIKI error fix for #61. Punctuation goes before References. Do general fixes if a problem exists. - using AWB (9916)
Line 1: Line 1:
A '''confidence band''' is used in [[statistics|statistical analysis]] to represent the uncertainty in an estimate of a curve or function based on limited or noisy data. Similarly, a '''prediction band''' is used to represent the uncertainty about the value of a new data-point on the curve, but subject to noise. Confidence and prediction bands are often used as part of the graphical presentation of results of a [[regression analysis]].  
There are several different alternatives to take into account while you are acquiring materials for the roof structure. In addition to choosing from the common components like timber, aluminum, porcelain tile or concrete roof covering, you can also look at reprocessed components. Solar panel systems may also be a possibility for people who desire to go green. Please read on for additional information!<br><br>


Confidence bands are closely related to [[confidence intervals]], which represent the uncertainty in an estimate of a single numerical value. "As confidence intervals, by construction, only refer to a single point, they are narrower (at this point) than a confidence band which is supposed to hold simultaneously at many points."<ref>p.65 in W. Härdle, M. Müller, S. Sperlich, A. Werwatz (2004), Nonparametric and Semiparametric Models, Springer, ISBN 3540207228 [http://sfb649.wiwi.hu-berlin.de/fedc_homepage/xplore/ebooks/html/spm/spmhtmlnode17.html],[http://books.google.com/books?id=qPCmAOS-CoMC&lpg=PA65&vq=As%20confidence%20intervals%2C%20by%20construction%2C%20only%20refer%20to%20a%20single%20point%2C%20they%20are%20narrower%20(at%20this%20point)%20than%20a%20confidence%20band%20which%20is%20supposed%20to%20hold%20simultaneously%20at%20many%20points&pg=PA65#v=snippet&q=As%20confidence%20intervals,%20by%20construction,%20only%20refer%20to%20a%20single%20point,%20they%20are%20narrower%20(at%20this%20point)%20than%20a%20confidence%20band%20which%20is%20supposed%20to%20hold%20simultaneously%20at%20many%20points&f=false]</ref>
You need to take into account the weather when picking a roofing variety. Clay roofing do well in dried up temperatures, plus they help in keeping the home awesome. In stormy climates, a clay roof top can deteriorate easily. When you are reluctant whether it will fit your area, check with an expert.<br><br>Remember that the spot on the floor, just beneath your roof structure, will take a bit of a whipping as your roof is changed. If you have blooms or some other shrubbery because region, it may get ruined. There may be nothing at all your roofing contractor are capable of doing to avoid it from going on, so attempt to avoid assigning fault.<br><br>In choosing between roofers, get hold of your community Much better Company Bureau for guidance. They will tell you if the organizations you are interested in have problems registered in opposition to them, a serious red flag. Also you can understand how very long they have been helping your group like a organization.<br><br>Will not pick the very first roofer you discover within the phone directory or on-line. By choosing the initially roofing contractor you learn about, you could turn out spending more income you need to. Get in touch with many roofing contractors and go along with probably the most dependable one particular in the very best selling price you can find.<br><br>Stay away from ice cubes build-through to your homes roof in the wintertime time. This possibly overwhelming condition takes place when snow starts to dissolve close to the indoor upholster of your property, then freezes, creating a close. That ice-cubes can remain for long periods of energy with reduced conditions and create leaks and warping. Appropriate air-flow and insulation ought to treatment the issue.<br><br>Following a thorough inspection and cleaning up from the roofing, it is actually important to area and close off any difficulty locations. Make certain that the weather conditions report shows nice weather conditions, due to the fact sealing components may take as much as two days and nights to totally heal. A sealant or another covering should be utilized once the places are treated.<br><br>When you see that your particular shingles are curling up or even buckling, it really is time for any new roof structure. When it might seem like a little issue to begin, once one shingle curls, the remainder will rapidly stick to. Have them all substituted to make sure you don't have and difficulties with leakages.<br><br>Check your rubber shoes on your roof top for cracking or dryness. This is a type of difficulty that rapidly brings about leakages around the roofing. Fortunately, they are super easy to fix and can be found at most of the neighborhood equipment stores. Even so, if you do not feel relaxed [http://Dict.Leo.org/?search=carrying carrying] it out your self you ought to undoubtedly contact a contractor.<br><br>The initial step to making the proper choice with regards to choosing roof structure material is learning about your possibilities. You might be already getting strides to creating your best option, particularly if you are operating over a a number of spending budget. Keep in mind recommendations in the following paragraphs when deciding on out your roofing material!<br><br>If you adored this article therefore you would like to be given more info with regards to [https://www.youtube.com/watch?v=XBIJi3PgpRg amherst roofing repair] i implore you to visit our web site.
 
==Pointwise and simultaneous confidence bands==
 
Suppose our aim is to estimate a function ''f(x)''.  For example, ''f(x)'' might be the proportion of people of a particular age ''x'' who support a given candidate in an election. If ''x'' is measured at the precision of a single year, we can construct a separate 95% confidence interval for each age. Each of these confidence intervals covers the corresponding true value ''f(x)'' with probability 0.95.  Taken together, these confidence intervals constitute a ''95% pointwise confidence band'' for ''f(x)''.
 
In mathematical terms, a pointwise confidence band <math>\hat{f}(x)\pm w(x)</math> with coverage probability 1&minus;α satisfies the following condition separately for each value of ''x'':
 
:<math>
{\rm Pr}\Big(\hat{f}(x)-w(x) \le f(x) \le \hat{f}(x)+w(x)\Big) = 1-\alpha,
</math>
 
where <math>\hat{f}(x)</math> is the point estimate of ''f''(''x'').
 
The ''simultaneous coverage probability'' of a collection of confidence intervals is the probability that all of them cover their corresponding true values simultaneously. In the example above, the simultaneous coverage probability is the probability that the intervals for x=18,19,... all cover their true values (assuming that 18 is the youngest age at which a person can vote).  If each interval individually has coverage probability 0.95, the simultaneous coverage probability is generally less than 0.95.  A ''95% simultaneous confidence band'' is a collection of confidence intervals for all values ''x'' in the domain of ''f(x)'' that is constructed to have simultaneous coverage probability 0.95. 
 
In mathematical terms, a simultaneous confidence band <math>\hat{f}(x)\pm w(x)</math> with coverage probability 1&minus;α satisfies the following condition:
 
:<math>
{\rm Pr}\Big(\hat{f}(x)-w(x) \le f(x) \le \hat{f}(x)+w(x) \;\;\;\; \text{ for all } x\Big) = 1-\alpha.
</math>
 
In nearly all cases, a simultaneous confidence band will be wider than a pointwise confidence band with the same coverage probability.
 
[[Image:binomial confidence band.svg|thumb|325px|Confidence bands for simulated data depicting the proportion of voters supporting a given candidate in election, as a function of the voters' ages. Pointwise 95% confidence bands, and simultaneous 95% confidence bands constructed using the [[Bonferroni method]] are shown.]]
 
==Confidence bands in regression analysis==
 
Confidence bands commonly arise in [[regression analysis]].<ref>{{cite journal |last= Liu|first= W|coauthors=Lin S., Piegorsch W.W.|year=2008| title= Construction of Exact Simultaneous Confidence Bands for a Simple Linear Regression Model|journal= International Statistical Review|volume=76| issue=1|pages=39&ndash;57|doi=10.1111/j.1751-5823.2007.00027.x }}</ref> In the case of a simple regression involving a single independent variable, results can be presented in the form of a plot showing the estimated regression line along with either point-wise or simultaneous confidence bands.  Commonly used methods for constructing simultaneous confidence bands in regression are the [[Bonferroni method|Bonferroni]] and [[Scheffé's method|Scheffé]] methods; see [[Familywise error rate#Controlling procedures|Familywise error rate controlling procedures]] for more.
 
[[Image:Regression confidence band.svg|thumb|325px|Confidence bands for a simple linear regression analysis using simulated data.  Pointwise 95% confidence bands, and simultaneous 95% confidence bands constructed using [[Scheffé's method]] are shown.]]
 
==Other applications of confidence bands==
 
Confidence bands arise whenever a statistical analysis focuses on estimating a function.
 
For example, confidence bands can be constructed around estimates of the [[empirical distribution function]]. Simple theory allows the construction of point-wise confidence intervals, but it is also possible to construct a simultaneous confidence band for the cumulative distribution function as a whole by inverting the [[Kolmogorov-Smirnov test#Setting confidence limits for the shape of a distribution function|Kolmogorov-Smirnov test]], or by using non-parametric likelihood methods
.<ref>{{cite journal |last=Owen |first= A.B. |year= 1995 |title=Nonparametric likelihood confidence bands for a distribution function |journal= Journal of the American Statistical Association|volume= 90|pages= 516&ndash;521| jstor=2291062 |doi=10.2307/2291062 |issue=430 |publisher=American Statistical Association}}</ref>
 
Confidence bands have also been devised for estimates of [[probability density function|density functions]], [[spectral density]] functions<ref>{{cite journal |last=Neumann | first=M.H.|coauthors=Paparoditis, E.|year=2008 |title=Simultaneous confidence bands in spectral density estimation|journal=Biometrika|volume=95|issue=2| doi=10.1093/biomet/asn005 |pages=381 }}</ref>
, [[quantile]] functions, [[smoothing|scatterplot smooths]], [[survival function]]s, and [[characteristic function (probability theory)|characteristic functions]]{{citation needed|date=April 2013}}.
 
==Prediction bands==
 
Prediction bands are related to [[prediction interval]]s in the same way that confidence bands are related to confidence intervals. Prediction bands commonly arise in regression analysis. The goal of a prediction band is to cover with a prescribed probability the values of one or more future observations from the same population from which a given data set was sampled. Just as prediction intervals are wider than confidence intervals, prediction bands will be wider than confidence bands.
 
In mathematical terms, a prediction band <math>\hat{f}(x)\pm w(x)</math> with coverage probability 1&minus;α satisfies the following condition for each value of ''x'':
 
:<math>
{\rm Pr}\Big(\hat{f}(x)-w(x) \le y^* \le \hat{f}(x)+w(x)\Big) = 1-\alpha,
</math>
 
where ''y''<sup>*</sup> is an observation taken from the data-generating process at the given point ''x'' that is independent of the data used to construct the point estimate <math>\hat{f}(x)</math> and the confidence interval ''w(x)''.  This is a pointwise prediction interval. It would be possible to construct a simultaneous interval for a finite number of independent observations using, for example, the Bonferroni method to widen the interval by an appropriate amount.
 
== References ==
{{reflist}}
 
{{Statistics}}
 
[[Category:Statistical inference]]

Revision as of 10:50, 6 February 2014

There are several different alternatives to take into account while you are acquiring materials for the roof structure. In addition to choosing from the common components like timber, aluminum, porcelain tile or concrete roof covering, you can also look at reprocessed components. Solar panel systems may also be a possibility for people who desire to go green. Please read on for additional information!

You need to take into account the weather when picking a roofing variety. Clay roofing do well in dried up temperatures, plus they help in keeping the home awesome. In stormy climates, a clay roof top can deteriorate easily. When you are reluctant whether it will fit your area, check with an expert.

Remember that the spot on the floor, just beneath your roof structure, will take a bit of a whipping as your roof is changed. If you have blooms or some other shrubbery because region, it may get ruined. There may be nothing at all your roofing contractor are capable of doing to avoid it from going on, so attempt to avoid assigning fault.

In choosing between roofers, get hold of your community Much better Company Bureau for guidance. They will tell you if the organizations you are interested in have problems registered in opposition to them, a serious red flag. Also you can understand how very long they have been helping your group like a organization.

Will not pick the very first roofer you discover within the phone directory or on-line. By choosing the initially roofing contractor you learn about, you could turn out spending more income you need to. Get in touch with many roofing contractors and go along with probably the most dependable one particular in the very best selling price you can find.

Stay away from ice cubes build-through to your homes roof in the wintertime time. This possibly overwhelming condition takes place when snow starts to dissolve close to the indoor upholster of your property, then freezes, creating a close. That ice-cubes can remain for long periods of energy with reduced conditions and create leaks and warping. Appropriate air-flow and insulation ought to treatment the issue.

Following a thorough inspection and cleaning up from the roofing, it is actually important to area and close off any difficulty locations. Make certain that the weather conditions report shows nice weather conditions, due to the fact sealing components may take as much as two days and nights to totally heal. A sealant or another covering should be utilized once the places are treated.

When you see that your particular shingles are curling up or even buckling, it really is time for any new roof structure. When it might seem like a little issue to begin, once one shingle curls, the remainder will rapidly stick to. Have them all substituted to make sure you don't have and difficulties with leakages.

Check your rubber shoes on your roof top for cracking or dryness. This is a type of difficulty that rapidly brings about leakages around the roofing. Fortunately, they are super easy to fix and can be found at most of the neighborhood equipment stores. Even so, if you do not feel relaxed carrying it out your self you ought to undoubtedly contact a contractor.

The initial step to making the proper choice with regards to choosing roof structure material is learning about your possibilities. You might be already getting strides to creating your best option, particularly if you are operating over a a number of spending budget. Keep in mind recommendations in the following paragraphs when deciding on out your roofing material!

If you adored this article therefore you would like to be given more info with regards to amherst roofing repair i implore you to visit our web site.

Retrieved from "https://en.formulasearchengine.com/index.php?title=Alpha_beta_filter&oldid=260336"