Indlela Yokuqalisa Izibalo
I-Pendahuluan
Izibalo yisayensi ehlose ukuqoqa, ukuhlaziya, ukuhumusha, nokwethula idatha. Ukuhlaziywa kwezibalo kuvame ukuncika ekucabangeni okuthile noma emibonweni yamathuba edinga osayizi abakhulu besampula ukuze kukhiqizwe izilinganiso ezinembile. Kodwa-ke, ezimweni eziningi, ukuthola amasampula amakhulu akusebenzi futhi akunakwenzeka. Yilapho indlela ye-bootstrap, inqubo yokuphinda isampula, iba usizo kakhulu.
Indlela ye-bootstrap yaqala ukwethulwa nguBradley Efron ngo-1979 futhi isibe ngenye yezindlela ezithandwa kakhulu kwizibalo ngenxa yokuguquguquka kwayo kanye nekhono lokukhiqiza izilinganiso ezinembile zamapharamitha amaningi abantu ngaphandle kokwenza izibikezelo ezithile zokusabalalisa. Lesi sihloko sizochaza izimiso eziyisisekelo zendlela ye-bootstrap, izinyathelo zayo zokusebenzisa, kanye nezibonelo eziningana zokusetshenziswa kwayo kwizibalo.
Izimiso Eziyisisekelo Zendlela Yokuqalisa
Indlela ye-bootstrap iyindlela engeyona i-parametric esivumela ukuthi silinganisele ukusatshalaliswa kwezibalo (isb., isilinganiso, i-median, i-variance) ngokuphinda sihlole idatha yethu yokuqala. Isimiso esiyisisekelo sale ndlela ukusebenzisa idatha ekhona (isampula yokuqala) ukulingisa amasethi amaningi edatha amasha ngokusampula okuphindaphindiwe.
Okulandelayo yizinyathelo eziyisisekelo ezithathwe endleleni ye-bootstrap:
1. Isampula Kabusha: Kusukela kusethi yedatha yokuqala yosayizi N, phinda usampula izikhathi N ngokufaka okunye esikhundleni. Lokhu kusho ukuthi izakhi ezikhethiwe ukuze zihlaziywe zingakhethwa ngaphezu kwesisodwa.
2. Bala Izibalo: Bala izibalo ozifunayo (isb., isilinganiso, isilinganiso) sesampula ngayinye.
3. Phinda Inqubo: Phinda izinyathelo 1 no-2 izikhathi eziningana (isb. B=1000 noma ngaphezulu) ukuze uthole ukusatshalaliswa kwe-bootstrap yezibalo onentshisekelo kuzo.
4. Ukulinganisa kanye nesiphetho: Sebenzisa lokhu kusatshalaliswa kwe-bootstrap ukudala izikhawu zokuzethemba, ukuhlola imibono, noma ukudala ezinye izibalo zokuphetha.
Izigaba Zokusebenzisa I-Bootstrap
Indlela ye-bootstrap ingachazwa ngokuningiliziwe kulezi zigaba ezilandelayo:
1. Ukuphinda kuthathwe amasampula
Ukuphinda uthayiphe ngokushintshana kuyingqikithi yendlela ye-bootstrap. Sisebenzisa idatha yokuqala, sakha amasethi amaningi edatha amasha, abizwa ngokuthi amasampula e-bootstrap. Isampula ngayinye ye-bootstrap ingumphumela wokuthatha amasampula izikhathi ze-N kusuka kusethi yedatha yokuqala yosayizi N, kodwa ngokushintshana, ukuze izakhi kusampula yokuqala zingavela kaningi kumasampula e-bootstrap.
Isibonelo:
Uma sinedatha yokuqala \[3, 5, 7, 9\], khona-ke isampula eyodwa ye-bootstrap engaba khona ingaba \[3, 9, 9, 5\].
2. Ukubala Izibalo ze-Bootstrap
Kusampula ngayinye ye-bootstrap, bala izibalo ozifunayo. Ake sithi sinesithakazelo ku-mean, singabala i-mean yesampula ngayinye ye-bootstrap. Uma siphinda le nqubo izikhathi ezingu-B, sizoba nezilinganiso zika-B ze-mean.
3. Ukwakha Ukusatshalaliswa Kwe-Bootstrap
Ngokuhlanganisa zonke izibalo ezibalwe kusukela kumasampula e-bootstrap e-B, sakha ukusatshalaliswa kwe-bootstrap kwezibalo ezifiselekayo. Lokhu kusatshalaliswa kusetshenziselwa ukulinganisa ukusatshalaliswa kwesampula kwezibalo.
4. Ukuphetha Ngezibalo
Kusukela kulokhu kusatshalaliswa kwe-bootstrap, singenza iziphetho ezahlukahlukene zezibalo. Isibonelo, singanquma izikhawu zokuzethemba ngokuthatha ama-percentile kusukela ekusatshalalisweni kwe-bootstrap noma sihlole ama-hypotheses ngokubheka inani le-p elitholwe kulokhu kusatshalaliswa.
Isibonelo Sokusebenzisa Indlela Ye-Bootstrap
Ukuze sinikeze isithombe esicacile, ake sibheke ezinye izibonelo zendlela indlela ye-bootstrap esetshenziswa ngayo ezimweni ezisebenzayo.
Isibonelo 1: Isikhawu Sokuqiniseka Esilinganiselwe
Ake sithi sinedatha yesampula yesisindo somzimba sabantu abayi-10 kanje: \[60, 62, 67, 70, 65, 68, 64, 60, 66, 63].
1. Kusukela kule datha, sithatha amasampula e-bootstrap ayi-1000 anobukhulu obufanayo, isibonelo:
– Isampula 1: \[62, 67, 70, 67, 64, 62, 63, 65, 68, 60\]
– Isampula 2: \[60, 62, 70, 70, 63, 64, 63, 65, 68, 62\]
- njll.…
2. Kusukela kusampula ngayinye ye-bootstrap, sibala isilinganiso:
– Isilinganiso sesampula 1: (62+67+70+67+64+62+63+65+68+60) / 10
– Isilinganiso sesampula 2: (60+62+70+70+63+64+63+65+68+62) / 10
- njll.…
3. Ngokuphinda lesi sinyathelo izikhathi eziyi-1000, sizothola isisindo esimaphakathi esiyi-1000.
4. Ngale datha eyisilinganiso esingu-1000, sakha ukusatshalaliswa kwe-bootstrap bese sithatha ama-percentile angu-2.5 kanye no-97.5 ukudala isikhawu sokuzethemba esingu-95%.
Isibonelo 2: Ukuhlolwa Kwe-Multiple Median Hypothesis
Ake sithi sifuna ukuhlola ukuthi ama-median amasethi amabili edatha ayalingana yini. Singasebenzisa i-bootstrapping ukudala ukusatshalaliswa komehluko kuma-median.
1. Thatha amasampula e-bootstrap kusuka kusethi ngayinye yedatha yokuqala.
2. Bala umehluko ophakathi nendawo wesampula ngayinye ye-bootstrap.
3. Dala ukusatshalaliswa komehluko ophakathi we-bootstrap.
4. Bheka ukuthi u-zero uwela yini ngaphakathi kwesikhawu sokuzethemba sokusabalalisa.
Izinzuzo kanye nokulinganiselwa kwendlela ye-Bootstrap
Ngokweqile
– Okungeyona ipharamitha: Akudingi ukuqagela mayelana nokusatshalaliswa kwedatha.
– Ukusebenza kahle kwamasampula amancane: Kusebenza kahle ngisho nasemasampula amancane.
– Iguquguqukayo: Ingasetshenziswa kuzibalo ezahlukahlukene kufaka phakathi isilinganiso, isilinganiso esimaphakathi, isilinganiso sokubuyela emuva, njll.
– Kulula Ukuyisebenzisa: Ngokuthuthuka kobuchwepheshe bekhompyutha, indlela ye-bootstrap kulula kakhulu ukuyisebenzisa ngosizo lwesofthiwe yezibalo efana ne-R noma i-Python.
Ukulinganiselwa
– Izindleko Zokubala: Kungadinga izinsiza eziningi zokubala ikakhulukazi ngosayizi wedatha omkhulu noma inani elikhulu lamasampula e-bootstrap (B).
– Ukuhlukahluka Kwesampula: Kufanelekile kuphela kumasampula amele ngokwanele inani labantu bokuqala.
– Akuvikeli Ukubandlulula: Uma idatha yokuqala inobandlululo, khona-ke wonke amasampula e-bootstrap azoba nobandlululo olufanayo.
Isiphetho
Indlela ye-bootstrap inikeza ikhambi elinamandla neliguquguqukayo ezinkingeni eziningi zokuphetha ngezibalo. Njengoba inekhono layo lokulinganisa kahle ukusatshalaliswa kwezibalo ezahlukene ngaphandle kokuthatha noma yikuphi ukusatshalaliswa okuthile, indlela ye-bootstrap isibe ithuluzi eliwusizo ekuhlaziyweni kwedatha. Naphezu kwemikhawulo yayo, izinzuzo ezinikezayo zivame ukwedlula izindleko zokubala. Uma isetshenziswa ngendlela efanele, indlela ye-bootstrap inganikeza ukuqonda okucebile nokunembile ngokuhlaziywa kwezibalo.
