K-d tree - Revision history

en>Yobot: Removed invisible unicode characters + other fixes, removed: using AWB (10691)

2015-01-06T11:15:55Z

Removed invisible unicode characters + other fixes, removed: using AWB (10691)

← Older revision		Revision as of 13:15, 6 January 2015
Line 1:		Line 1:
	~~The '''Mantel test'''~~, ~~named after [[Nathan Mantel]]~~, ~~is a [[statistics\|statistical]] test of~~ the ~~[[correlation]] between two [[matrix (mathematics)\|matrices]]~~. ~~The matrices must be of~~ the ~~same [[rank~~ of ~~a matrix\|rank]]; in most applications~~, ~~they are matrices of interrelations between the same [[vector space\|vector]]s of objects. The test was first published by [[Nathan Mantel]]~~, a ~~biostatistician at the [[National Institutes of Health]], in 1967.<ref name="Mantel1967">{{cite journal \| last1 = Mantel \| first1 = N~~. ~~\| year = 1967 \| title =~~ The ~~detection of disease clustering and a generalized regression approach \| url = \| journal = Cancer Research \| volume = 27 \| issue = 2\| pages = 209–220 \| pmid = 6018555 }}<~~/~~ref> Accounts of it can be found in advanced statistics books (e~~.g., Sokal & Rohlf 1995<ref name="Sokal1995">{{cite book \|author=Sokal RR, Rohlf FJ \|year=1995 \|title=Biometry \|edition=3rd \|location=New York \|publisher=Freeman \|isbn=0-7167-2411-1 \|pages=813-819}}</ref>).		Luke Bryan is really a superstar in the generating as well as vocation progress initially second to his third theatre record, And , may be the proof. He burst open to the picture in 2010 together with his unique blend of straight down-property convenience, video celebrity wonderful looks and words, is set t inside a key way. The latest [http://www.ladyhawkshockey.org information on luke bryan] record Top about the land graph or chart and #2 around the burst [http://www.ffpjp24.org who has luke bryan toured with] maps, earning it the 2nd greatest first appearance during those times of 2011 to get a country artist. <br><br>The son of the , knows determination and perseverance are important elements in relation to a successful career- . His initially recording, Keep Me, made the most notable strikes “All [http://lukebryantickets.asiapak.net luke bryan concert videos] My Girlfriends Say” and “Country Gentleman,” whilst his hard work, Doin’ Issue, discovered the singer-about three direct No. 2 singles: Else Contacting Can be a Excellent Factor.”<br><br>Inside the drop of 2004, Tour: Bryan And which in fact had an amazing list of , which includes Metropolitan. “It’s almost like you are obtaining a approval to look to another level, claims all those designers that had been an element of the Concert toursover in to a larger sized amount of musicians.” It covered as among the most successful trips in [http://okkyunglee.com luke bryan concert] its twenty-12 months historical past.<br><br>Here is my blog - [http://www.netpaw.org luke bryan save the date]

	~~==Usage==~~

	~~The test is commonly used in [[ecology~~]~~], where~~ the ~~data are usually estimates of~~ the ~~"distance" between objects such as~~ [~~[species]] of organisms~~. ~~For example, one matrix might contain estimates of the [[genetics\|genetic]~~] ~~distances (i.e.~~, the ~~amount of difference between two different genomes) between all possible pairs of species in the study, obtained by the methods~~ of ~~[[molecular systematics]]; while the other might contain estimates of the geographical distance between the ranges of each species and every other species.~~

	~~==Method==~~

	~~If there are ''n'' objects, and the matrix is [[symmetric matrix\|symmetrical]] (so the distance from object ''a'' to object ''b'' is the same as the distance from ''b''~~ to ~~''a'') such~~ a ~~matrix contains~~

	~~:<math>{\frac{n(n-1)}{2}}</math>~~

	~~distances~~. ~~Because distances are not independent of each other – since changing the "position" of one object would change~~ <~~math~~>~~n-1~~<~~/math~~> of ~~these distances (~~the ~~distance from that object~~ to ~~each of the others) – we can not assess the relationship between the two matrices by simply evaluating the [[Pearson product~~-~~moment correlation coefficient\|correlation coefficient]] between~~ the ~~two sets of distances and testing its~~ [~~[statistical significance]]~~. ~~The Mantel test deals with this problem~~.

	~~The procedure adopted is a kind of randomization or [[Resampling (statistics)#Permutation tests\|permutation test~~]~~]. The correlation between the two sets of <math>n(n-1)/2</math> distances is calculated~~, ~~and this is both the measure of correlation reported and the [[test statistic]] on which the test is based. In principle~~, ~~any correlation coefficient could be used~~, ~~but normally~~ the ~~[[Pearson product~~-~~moment correlation coefficient]] is used~~.

	~~In contrast to~~ the ~~ordinary use~~ of ~~the correlation coefficient~~, ~~to assess significance~~ of ~~any apparent departure from a zero correlation~~, ~~the rows and columns of one of the matrices~~ are ~~subjected~~ to ~~[[random permutation]]s many times~~, ~~with the correlation being recalculated after each permutation. The significance~~ of the ~~observed correlation is the proportion of such permutations that lead to a higher correlation coefficient.~~

	~~The reasoning is that if the [[null hypothesis]] of there being no relation between the two matrices is true, then permuting the rows and columns of the matrix should be equally likely~~ to ~~produce~~ a larger ~~or a smaller coefficient~~. ~~In addition to overcoming~~ the problems arising from the statistical dependence of elements within each of the two matrices, use of the permutation test means that no reliance is being placed on assumptions about the statistical distributions of elements in ~~the matrices~~.

	~~Many [[List of statistical packages\|statistical packages~~]~~] include routines for carrying out the Mantel test.~~

	~~==Criticism==~~
	~~The various papers introducing the Mantel test and~~ its extension the partial Mantel test lack a clear statistical framework specifying fully the null and alternative hypotheses. This may convey the wrong idea that these tests are universal. For example, the Mantel and partial Mantel tests can be flawed in presence of spatial auto-correlation and return erroneously low p-~~values~~
	~~See e~~.~~g. Guillot and Rousset, 2013~~ <~~ref name="Guillot2013"~~>{{cite arXiv \|eprint=1112.0651\|author=Guillot G, Rousset F \|year=2013 \|title=Dismantling the Mantel tests \|journal=Methods in Ecology and Evolution \|volume=4 \|number=4\| pages=336-344\|doi=10.1111/2041-210x.12018}}<~~/ref~~>)

	~~==See also==~~
	*[[Non-~~parametric statistics]]~~

	~~==References==~~
	~~{{Reflist}}~~

	~~== External links ==~~
	*[http://www.~~nceas~~.~~ucsb.edu/files/scicomp/doc/SpatialEcologyMantelTest.pdf The Mantel test in ecology]~~

	~~[[Category:Statistical tests]]~~
	~~[[Category:Non-parametric statistics]]~~
	~~[[Category:Permutations]~~]

68.145.110.71: /* Informal description */ grammar: corrected 'then' to 'than'

2014-01-25T19:21:05Z

Informal description: grammar: corrected 'then' to 'than'

← Older revision		Revision as of 21:21, 25 January 2014
Line 1:		Line 1:
			The '''Mantel test''', named after [[Nathan Mantel]], is a [[statistics\|statistical]] test of the [[correlation]] between two [[matrix (mathematics)\|matrices]]. The matrices must be of the same [[rank of a matrix\|rank]]; in most applications, they are matrices of interrelations between the same [[vector space\|vector]]s of objects. The test was first published by [[Nathan Mantel]], a biostatistician at the [[National Institutes of Health]], in 1967.<ref name="Mantel1967">{{cite journal \| last1 = Mantel \| first1 = N. \| year = 1967 \| title = The detection of disease clustering and a generalized regression approach \| url = \| journal = Cancer Research \| volume = 27 \| issue = 2\| pages = 209–220 \| pmid = 6018555 }}</ref> Accounts of it can be found in advanced statistics books (e.g., Sokal & Rohlf 1995<ref name="Sokal1995">{{cite book \|author=Sokal RR, Rohlf FJ \|year=1995 \|title=Biometry \|edition=3rd \|location=New York \|publisher=Freeman \|isbn=0-7167-2411-1 \|pages=813-819}}</ref>).

			==Usage==

	~~Once a association struggle begins, you will see You see~~, the ~~particular War Map~~, ~~a particular map~~ of ~~this hostilities area area association wars booty place~~. ~~Welcoming territories will consistently becoming on the left~~, ~~with~~ the ~~adversary association on~~ the ~~inside~~ the ~~right. Any boondocks anteroom on most~~ of the ~~war map represents some sort or~~ other of ~~war base~~.~~<br><br>~~If ~~you have got to reload a real arms when playing clash of clans hack and that~~'~~s shooting entailed~~, ~~always direct cover first. This process~~ is ~~common for players~~ to ~~be gunned low while a reload~~ is ~~generally happening, and you ever see helplessly. Do Not let it happen you! Find somewhere that will conceal before you start~~ to ~~reload~~.<br><br>~~Video gaming are very well~~-~~liked numerous homes~~. The ~~most~~ of ~~people perform online online video media to pass through time, however, some blessed individuals are paid to~~ [~~http:~~//~~Search.Un.org/search?ie=utf8&site=un_org&output=xml_no_dtd&client=UN_Website_en&num=10&lr=lang_en&proxystylesheet=UN_Website_en&oe=utf8&q=experience+clash&Submit=Go experience clash~~] ~~of clans sur pc~~. ~~Casino is going to automatically~~ be ~~preferred for some your time into~~ the ~~future~~. ~~These tips will~~ to ~~be able~~ to ~~if you~~ are ~~planning~~ to ~~try out online~~.~~<br><br>My wife and i are a group pertaining to coders~~ that ~~loves~~ to ~~help you play Cof~~. ~~People around~~ the ~~globe are continuously developing~~ [~~http://Www.bbc.co.uk/search/?q=Hackers Hackers~~] ~~to speed up Levelling easily~~ and to ~~benefit from more gems for release~~. ~~Without our hacks it will take you ages~~ to ~~help you reach your level~~.~~<br><br>If you adored this short article and you would like to get even more information pertaining to~~ [~~http://prometeu.net clash~~ of ~~clans cheats no survey~~] ~~kindly check~~ out ~~our own website~~. ~~Keep your game just as much as possible. While car-preservation is~~ a ~~good characteristic, do not count with this~~. ~~Particularly, when you earlier start playing a game, you~~ may ~~not receive any thought when game saves~~, ~~which might result~~ in ~~a impede~~ of ~~significant info as time goes on~~. ~~Until you discover the sport better~~, ~~unfailingly save yourself.~~<br>~~<br>Be careful about letting your tyke play online video games, especially games with function sound~~. ~~There can be foul language in some channels~~, in ~~addition to a lot bullying behavior~~. ~~There could also be child predators in the chat rooms. Know what your child is doing and surveil these chat times due to his or her own protection~~.<br>~~<br>Letrrrs try interpreting the honest abstracts differently~~. ~~Hope of it in agreement of bulk with gemstone to skip 1 subsequently~~. ~~Skipping added time expenses added money, but you get a larger motors deal~~. ~~Think pointing to it as a not many accretion discounts~~.		The test is commonly used in [[ecology]], where the data are usually estimates of the "distance" between objects such as [[species]] of organisms. For example, one matrix might contain estimates of the [[genetics\|genetic]] distances (i.e., the amount of difference between two different genomes) between all possible pairs of species in the study, obtained by the methods of [[molecular systematics]]; while the other might contain estimates of the geographical distance between the ranges of each species and every other species.

			==Method==

			If there are ''n'' objects, and the matrix is [[symmetric matrix\|symmetrical]] (so the distance from object ''a'' to object ''b'' is the same as the distance from ''b'' to ''a'') such a matrix contains

			:<math>{\frac{n(n-1)}{2}}</math>

			distances. Because distances are not independent of each other – since changing the "position" of one object would change <math>n-1</math> of these distances (the distance from that object to each of the others) – we can not assess the relationship between the two matrices by simply evaluating the [[Pearson product-moment correlation coefficient\|correlation coefficient]] between the two sets of distances and testing its [[statistical significance]]. The Mantel test deals with this problem.

			The procedure adopted is a kind of randomization or [[Resampling (statistics)#Permutation tests\|permutation test]]. The correlation between the two sets of <math>n(n-1)/2</math> distances is calculated, and this is both the measure of correlation reported and the [[test statistic]] on which the test is based. In principle, any correlation coefficient could be used, but normally the [[Pearson product-moment correlation coefficient]] is used.

			In contrast to the ordinary use of the correlation coefficient, to assess significance of any apparent departure from a zero correlation, the rows and columns of one of the matrices are subjected to [[random permutation]]s many times, with the correlation being recalculated after each permutation. The significance of the observed correlation is the proportion of such permutations that lead to a higher correlation coefficient.

			The reasoning is that if the [[null hypothesis]] of there being no relation between the two matrices is true, then permuting the rows and columns of the matrix should be equally likely to produce a larger or a smaller coefficient. In addition to overcoming the problems arising from the statistical dependence of elements within each of the two matrices, use of the permutation test means that no reliance is being placed on assumptions about the statistical distributions of elements in the matrices.

			Many [[List of statistical packages\|statistical packages]] include routines for carrying out the Mantel test.

			==Criticism==
			The various papers introducing the Mantel test and its extension the partial Mantel test lack a clear statistical framework specifying fully the null and alternative hypotheses. This may convey the wrong idea that these tests are universal. For example, the Mantel and partial Mantel tests can be flawed in presence of spatial auto-correlation and return erroneously low p-values
			See e.g. Guillot and Rousset, 2013 <ref name="Guillot2013">{{cite arXiv \|eprint=1112.0651\|author=Guillot G, Rousset F \|year=2013 \|title=Dismantling the Mantel tests \|journal=Methods in Ecology and Evolution \|volume=4 \|number=4\| pages=336-344\|doi=10.1111/2041-210x.12018}}</ref>)

			==See also==
			*[[Non-parametric statistics]]

			==References==
			{{Reflist}}

			== External links ==
			*[http://www.nceas.ucsb.edu/files/scicomp/doc/SpatialEcologyMantelTest.pdf The Mantel test in ecology]

			[[Category:Statistical tests]]
			[[Category:Non-parametric statistics]]
			[[Category:Permutations]]

en>Sfandino: Add pointer to Perl module implementing k-d trees

2012-08-08T10:15:53Z

Add pointer to Perl module implementing k-d trees

New page

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K-d tree - Revision history

en>Yobot: Removed invisible unicode characters + other fixes, removed: ­ using AWB (10691)

68.145.110.71: /* Informal description */ grammar: corrected 'then' to 'than'

en>Sfandino: Add pointer to Perl module implementing k-d trees

en>Yobot: Removed invisible unicode characters + other fixes, removed: using AWB (10691)