Ngā Tikanga Whakatau Tatau i roto i ngā Tatauranga
He ariā taketake te whakatau tata i roto i ngā tatauranga, e tautoko ana i te kaha ki te whakatau whakatau mō tētahi taupori i runga i ngā raraunga tauira. I tēnei ao e kī ana i ngā raraunga, ka whakawhirinaki ngā tohunga tatauranga ki ngā momo tikanga whakatau tata hei whiwhi māramatanga whai tikanga. Ka rukuhia e tēnei tuhinga ētahi o ngā tikanga whakatau tata e whakamahia whānuitia ana, ō rātou mātāpono, ō rātou painga, me ngā āhuatanga e tino tika ana.
Kupu Whakataki ki te Whakatau Tatau
Ko te whāinga matua o te whakatau tata i roto i ngā tatauranga ko te whakatau tata i ngā tawhā taupori (pēnei i te toharite, te rerekētanga, me ētahi atu) mā te whakamahi i ngā tatauranga tauira. Nā te mea he maha ngā wā kāore e taea te tātari i tētahi taupori katoa, ka taea e ngā tikanga whakatau tata te whakatau whakaaro mō ngā āhuatanga o te taupori.
Te Whakatau i ngā Pūwāhi
Ko te whakatau tata ira he whakarato i tētahi uara kotahi hei whakatau tata mō tētahi tawhā taupori. Hei tauira, ko te toharite tauira (𝑥̄) e whakamahia ana hei whakatau tata mō te toharite taupori (μ). Ahakoa he māmā noa iho, he ngāwari hoki, he iti noa iho ngā herenga o ngā whakatau tata: kāore e whakarato i ngā mōhiohio mō te koretake, te rerekētanga rānei o te whakatau tata.
Ngā Tikanga Whakatau Ira Rongonui
1. Tikanga o ngā Wā:
Ko te tikanga o ngā wā poto ko te whakataurite i ngā wā poto tauira ki ngā wā poto taupori. Ko ngā wā poto he pūmau tatauranga e whakarato ana i te māramatanga ki te āhua me ngā āhuatanga o te tohatoha tūponotanga. Ko te tikanga, ka whakatauritehia e tēnei tikanga ngā wā poto ariā (pēnei i te toharite, te rerekētanga) ki ō rātou hoa tauira hei whakaputa whakatau tata.
2. Te Whakatau Tatau Tūponotanga Mōrahi (MLE):
He tikanga whakatau tata pakari, whānuitia hoki te MLE e whakatau ana i ngā whakatau tata tawhā mā te whakanui ake i te mahi tūponotanga. Ka ine te mahi tūponotanga i te whaitake o ngā tawhā i runga i ngā raraunga kua kitea. E mōhiotia ana ngā tātai tata MLE mō ō rātou āhuatanga e hiahiatia ana, pērā i te ōritetanga, te whai huatanga, me te āhua noa o te koretake.
3. Te Whakatau Tatau Bayesian:
Ka whakauruhia e te whakatau tata Bayesian ngā whakapono o mua, ngā mōhiotanga rānei mō tētahi tawhā me ngā raraunga kua kitea. Mā te tohatoha o muri (he ranunga o te tohatoha o mua me te tūponotanga) ka whakaratohia he whakarāpopototanga whānui o te koretake o te tawhā. He tino kaha ngā tikanga Bayesian i roto i te ako auau me te wā e pā ana ki ngā tauira uaua, ngā raraunga iti rānei.
Te Whakatau i te Wā
He rerekē te whakatau tata i te ira, ka whakaratohia e te whakatau tata i te whānuitanga o ngā uara e taea ai te taka o te tawhā, e whakaatu ana i te koretake o roto i tētahi tukanga whakatau tata. Ko ngā wā whakawhirinaki me ngā wā pono (i roto i ngā horopaki Bayesian) ngā momo matua e rua.
1. Ngā Wā Whakawhirinaki:
He whānuitanga o ngā uara kei roto i te āputa whakawhirinaki, i tatauhia mai i ngā raraunga tauira, e tūpono ana kia mau te tawhā taupori me te taumata whakawhirinaki kua tohua (hei tauira, 95%). Ko te hanganga o ngā āputa whakawhirinaki e uru ana ki te hapa paerewa o te whakatau tata me te uara nui mai i te tohatoha tūponotanga e tika ana.
2. Ngā Wā Whakapono:
I roto i ngā tatauranga Bayesian, ko te āputa pono ko te awhe e taka ai te uara tawhā kāore i kitea me tētahi tūponotanga, i runga i ngā raraunga i kitea. Kāore i rite ki ngā āputa pono auau, he māmā ake te whakamārama i ngā āputa pono, ā, he māmā ake te whakapuaki i ngā tauākī tūponotanga.
Ngā Āhuatanga o ngā Kaiwhakatau Tatau
I te wā e whiriwhiri ana, e aromatawai ana hoki i ngā tikanga aromatawai, ka puta ake ētahi āhuatanga:
1. Te kore whakaaro nui:
He kore whakaaro pākiki te tātaitanga mēnā he ōrite te uara e tumanakohia ana o te tātaitanga ki te uara tawhā tūturu. Ko te tikanga, he kore whakaaro pākiki te tātaitanga $\hat{\theta}$ o te tawhā $\theta$ mēnā $E(\hat{\theta}) = \theta$. Kāore ngā tātaitanga kore whakaaro pākiki e whakanui rawa, e whakaiti rānei i ngā tawhā.
2. Te ōritetanga:
He rite tonu te whakatau tata mēnā ka piki ake te rahi o te tauira, ka taurite te tūponotanga ki te uara tawhā tūturu. Mā te rite tonu ka puta he whakatau tata e tata ana ki te tawhā tūturu i ngā tauira nui ake.
3. Whai huatanga:
I roto i tētahi akomanga o ngā kaiwhakatau whakatau tata kore whakaaro, ko te kaiwhakatau whakatau tino whai hua ko te mea he iti rawa te rerekētanga. He mea nui te whai huatanga hei whakaiti i te hapa whakatau tata me te whakarei ake i te tika.
4. Te Rawaka:
He rawaka te tātaitanga mēnā ka hopukina e ia ngā mōhiohio katoa mō ngā tawhā kei roto i ngā raraunga tauira. Mā ngā tātaitanga e ranea ana ka whakarapopototia te mauri o ngā raraunga e pā ana ki te tawhā e hiahiatia ana, ā, kāore he mōhiohio e tika ana e mahue ana.
5. Pakari:
Ko te pakari e pā ana ki te kore aro o te kaiwhakatau ki ngā takahi i ngā whakapae, ki te aroaro rānei o ngā mea kāore i te tino kitea. He mea nui ngā kaiwhakatau pakari i roto i ngā tono o te ao tūturu ina kore e tino kitea ngā āhuatanga pai.
Te Whakamahinga Whaihua o ngā Tikanga Whakatau Tatau
Te Kōwhiri i te Tikanga Whakatau Tatau e Tika ana
Ko te whiriwhiri i tētahi tikanga aromatawai tika e whakawhirinaki ana ki ētahi āhuatanga:
1. Te Āhua o ngā Raraunga me te Tohatoha Taketake:
Mena kei te wātea ngā mōhiotanga o mua mō te tohatoha, ka taea e ia te ārahi i te whiriwhiri i te tikanga. Hei tauira, he tino pai te MLE ina mōhiotia te āhua o te mahi tūponotanga.
2. Rahi Tauira:
Ka pā te rahi o te tauira ki te whakamahinga me te mahi a ngā tikanga whakatau tata rerekē. Ko ētahi tikanga, pērā i te MLE me te whakatau tata Bayesian, ka pai ake te mahi me ngā tauira nui ake, engari ko ngā tikanga pērā i te tikanga o ngā wā ka taea te whakamahi ki ngā tauira iti ake.
3. Ngā Rauemi Tātari:
Ka taea e ngā tikanga uaua, inā koa ko ngā huarahi Bayesian, te whakamahi i te kaha ki te tatau. Ko te wātea o ngā rauemi tatau me ngā herenga wā ka ārahi pea i te whiriwhiri i te tikanga whakatau tata.
4. Te aroaro o ngā Mōhiohio o Mua:
He pai te whakatau tata Bayesian ina wātea ngā mōhiohio o mua mō ngā tawhā, ā, ka taea te ine. He rerekē, ko ngā tikanga auau pēnei i te MLE, i te tikanga rānei o ngā wā, kāore e whakauru i ngā mōhiohio o mua.
Tauira: Te Whakatau Tatau o te Toharite
Whakaarohia tētahi tauira e whai ana mātou ki te whakatau tata i te toharite μ o tētahi taupori tohatoha noa i runga i tētahi tauira:
1. Te Whakatau Tatau Pūwāhi:
– Tauira Toharite ($\hat{\mu} = \bar{x}$): Koinei te whakatau tata tino māmā o μ.
2. Te Whakatau i te Wā:
– Wā Whakawhirinakitanga: Mena ka whakamahia te rerekētanga tauira (s²) hei whakatau tata i te rerekētanga taupori (σ²), ka taea te tatau i te wā whakawhirinakitanga (1-α)% mō te toharite mā te whakamahi i te tohatoha-t:
$$
\bar{x} \pm t_{\alpha/2, n-1} \left(\frac{s}{\sqrt{n}}\right)
$$
– Wā Whakapono Bayesian: Mena ka whakaarohia he tohatoha o mua mō μ, ka taea te whakaputa i tētahi wā pono mai i te tohatoha o muri.
Opaniraa
He taputapu tino nui ngā tikanga whakatau tata i roto i ngā tatauranga hei whakatau whakatau mō ngā tawhā taupori i runga i ngā raraunga tauira. Mai i te tikanga kore mārama o ngā wā ki te tikanga tino matatau o te tūponotanga mōrahi me ngā huarahi Bayesian, he painga me ngā whakamahinga o ia tikanga. Mā te mārama ki ngā āhuatanga me ngā horopaki tika mō ēnei tikanga ka taea e ngā kaitātari tatauranga te whakatau tata whai whakaaro me te tika, ā, ka puta he māramatanga whai tikanga mai i ngā raraunga. Ahakoa te tautohetohe ki ngā rahi tauira iti, ki ngā huinga raraunga nui rānei, ko te toi me te pūtaiao o te whakatau tata kei te ngako tonu o te tātari tatauranga.
