Hanyar Bootstrap a cikin Ƙididdiga
Pendahuluan
Kididdiga ita ce kimiyyar da ke da nufin tattarawa, yin nazari, fassarawa, da kuma gabatar da bayanai. Binciken kididdiga sau da yawa ya dogara ne akan wasu zato ko ka'idojin yiwuwar da ke buƙatar manyan girman samfura don samar da kimantawa daidai. Duk da haka, a yanayi da yawa, samun manyan samfura ba abu ne mai amfani ba kuma ba zai yiwu ba. Nan ne hanyar bootstrap, wata dabarar sake yin samfura, ta zama mai matuƙar amfani.
Bradley Efron ne ya fara gabatar da hanyar bootstrap a shekarar 1979 kuma ta zama ɗaya daga cikin shahararrun dabarun kididdiga saboda sassauci da ikonta na samar da kimantawa daidai ga ma'aunin yawan jama'a da yawa ba tare da yin takamaiman zato na rarrabawa ba. Wannan labarin zai bayyana ƙa'idodin asali na hanyar bootstrap, matakan aiwatarwa, da misalai da dama na aikace-aikacenta a cikin ƙididdiga.
Ka'idojin Asali na Hanyar Bootstrap
Hanyar bootstrap hanya ce da ba ta da ma'auni wadda ke ba mu damar kimanta rarrabawar ƙididdiga (misali, matsakaici, matsakaici, bambancin) ta hanyar sake yin samfurin bayananmu na asali. Babban ƙa'idar wannan hanyar ita ce amfani da bayanan da ke akwai (samfurin asali) don kwaikwayon sabbin saitunan bayanai da yawa tare da maimaita samfurin.
Ga matakan da aka ɗauka a cikin hanyar bootstrap:
1. Sake samfuri: Daga saitin bayanai na asali na girman N, sake samfurin N sau tare da maye gurbinsa. Wannan yana nufin cewa abubuwan da aka zaɓa don bincike za a iya zaɓar su fiye da sau ɗaya.
2. Lissafin Kididdiga: Lissafa kididdigar da ake so (misali, matsakaici, matsakaici) ga kowane sake samfurin.
3. Maimaita Tsarin: Maimaita matakai na 1 da 2 sau da yawa (misali B=1000 ko fiye) don samun rarrabawar ƙididdiga da kake sha'awar.
4. Kimantawa da Kammalawa: Yi amfani da wannan rarrabawar bootstrap don ƙirƙirar tazara ta amincewa, gwada hasashe, ko ƙirƙirar wasu ƙididdiga na tunani.
Matakan Aiwatar da Bootstrap
Ana iya bayyana hanyar bootstrap dalla-dalla a cikin matakai masu zuwa:
1. Sake yin samfur
Sake yin samfuri tare da maye gurbin shine ainihin hanyar bootstrap. Ta amfani da bayanan asali, muna ƙirƙirar sabbin saitin bayanai da yawa, waɗanda ake kira samfuran bootstrap. Kowane samfurin bootstrap sakamakon samfurin N sau N ne daga saitin bayanan asali na girman N, amma tare da maye gurbin, don haka abubuwan da ke cikin samfurin asali na iya bayyana fiye da sau ɗaya a cikin samfuran bootstrap.
Misali:
Idan muna da ainihin bayanan \[3, 5, 7, 9\], to, samfurin bootstrap ɗaya zai iya zama \[3, 9, 9, 5\].
2. Lissafin Kididdigar Bootstrap
Ga kowane samfurin bootstrap, ƙididdige ƙididdigar da ake so. A ce muna da sha'awar matsakaicin, za mu ƙididdige matsakaicin kowane samfurin bootstrap. Idan muka maimaita wannan tsari sau B, za mu sami kimantawar B na matsakaicin.
3. Samar da Rarraba Bootstrap
Ta hanyar tattara dukkan kididdigar da aka ƙididdige daga samfuran B bootstrap, muna gina rarrabawar bootstrap na ƙididdigar da ake so. Ana amfani da wannan rarraba don kimanta rarrabawar samfurin ƙididdiga.
4. Ka'idar Ƙididdiga
Daga wannan rarrabawar bootstrap, za mu iya yin ƙididdiga daban-daban. Misali, za mu iya ƙayyade tazara ta amincewa ta hanyar ɗaukar kashi-kashi daga rarrabawar bootstrap ko gwada hasashe ta hanyar duba ƙimar p da aka samu daga wannan rarraba.
Misali na Amfani da Hanyar Bootstrap
Domin samar da hoto mai haske, bari mu dubi wasu misalai na yadda ake amfani da hanyar bootstrap a cikin mahallin aiki.
Misali na 1: Matsakaicin Tazarar Amincewa
A ce muna da samfurin bayanai na nauyin jikin mutum 10 kamar haka: \[60, 62, 67, 70, 65, 68, 64, 60, 66, 63\].
1. Daga wannan bayanin, mun ɗauki samfuran bootstrap guda 1000 masu girman iri ɗaya, misali:
– Samfurin 1: \[62, 67, 70, 67, 64, 62, 63, 65, 68, 60\]
– Samfurin 2: \[60, 62, 70, 70, 63, 64, 63, 65, 68, 62\]
- da sauransu…
2. Daga kowace samfurin bootstrap, muna ƙididdige matsakaicin:
– Misalin Ma'auni 1: (62+67+70+67+64+62+63+65+68+60) / 10
– Misalin Ma'auni 2: (60+62+70+70+63+64+63+65+68+62) / 10
- da sauransu…
3. Ta hanyar maimaita wannan matakin sau 1000, za mu sami matsakaicin nauyi 1000.
4. Da waɗannan matsakaicin bayanai 1000, mun samar da rarrabawar bootstrap kuma muka ɗauki kashi 2.5 da 97.5 don ƙirƙirar tazara ta amincewa da kashi 95%.
Misali na 2: Gwajin Hasashe Tsakanin Matsakaici da Yawa
A ce muna son gwada ko matsakaicin saitin bayanai guda biyu daidai yake. Za mu iya amfani da bootstrapping don ƙirƙirar rarraba bambancin a cikin matsakaici.
1. Ɗauki samfuran bootstrap daga kowanne daga cikin saitunan asali.
2. Lissafa matsakaicin bambanci ga kowane samfurin bootstrap.
3. Ƙirƙiri rarraba bambance-bambancen matsakaici na bootstrap.
4. Duba ko sifili ya faɗi cikin tazara ta amincewa ta rarrabawa.
Amfani da Iyakoki na Hanyar Bootstrap
wuce gona da iri
– Ba a daidaita shi ba: Ba ya buƙatar zato game da rarraba bayanai.
– Inganci ga Ƙananan Samfura: Mai tasiri ko da ga ƙananan samfura.
- Mai sassauƙa: Ana iya amfani da shi ga ƙididdiga daban-daban, gami da matsakaicin, matsakaicin, ma'aunin komawa baya, da sauransu.
– Sauƙin Aiwatarwa: Tare da ci gaban fasahar kwamfuta, hanyar bootstrap tana da sauƙin aiwatarwa tare da taimakon software na ƙididdiga kamar R ko Python.
Iyakance
– Kudin Kwamfuta: Yana iya buƙatar albarkatun kwamfuta da yawa musamman tare da manyan bayanai ko adadi mai yawa na samfuran bootstrap (B).
– Bambancin Samfura: Ya dace ne kawai da samfuran da suka isa wakilcin mutanen asali.
– Ba Ya Kare Kariya Daga Son Zuciya: Idan bayanan asali suna da son zuciya, to duk samfuran bootstrap za su ƙunshi son zuciya iri ɗaya.
Kammalawa
Hanyar bootstrap tana ba da mafita mai ƙarfi da sassauƙa ga matsalolin ƙididdiga da yawa. Tare da ikonta na ƙididdige rarraba ƙididdiga daban-daban yadda ya kamata ba tare da ɗaukar wani takamaiman rarrabawa ba, hanyar bootstrap ta zama kayan aiki mai mahimmanci a cikin nazarin bayanai. Duk da iyakokinta, fa'idodin da take bayarwa galibi sun fi farashin lissafi. Idan aka yi amfani da su yadda ya kamata, hanyar bootstrap na iya samar da fahimta mai kyau da daidaito game da nazarin ƙididdiga.
