He aha ngā Tatauranga Bayesian?
Ko ngā tatauranga Bayesian, i tapaina i muri i te tohunga pāngarau o te rautau 18, a Thomas Bayes, e tohu ana i tētahi panonitanga tauira i roto i te mara o te whakatau tatauranga. He rerekē ki ngā huarahi auau tuku iho, ka tukuna e ngā tatauranga Bayesian tētahi anga ahurei mō te whakahou i te tūponotanga o tētahi ariā i runga i ngā taunakitanga hou. I runga i te Ariā a Bayes, ka taea e tēnei huarahi te mārama ake ki ngā raraunga me tētahi tauira ngāwari ake o te koretake. Ka rukuhia e tēnei tuhinga ngā mātāpono, ngā tono, me ngā painga o ngā tatauranga Bayesian, e whakaatu ana i te āhua o tana whakahou i te whenua o te tātari raraunga me te whakatau kaupapa.
Ngā Kaupapa Taketake o ngā Tatauranga Bayesian
I tōna pūtake, ko ngā tatauranga Bayesian e aro ana ki te ariā a Bayes, e whakaahua ana i te whanaungatanga i waenga i ngā tūponotanga ā-tikanga. Ka taea te kī i te ariā penei:
\[ P(A|B) = \frac{P(B|A) \cdot P(A)}{P(B)} \]
Kei hea:
– Ko te tūponotanga o muri ko te \( P(A|B) \): te tūponotanga o te whakapae \( A \) i runga i ngā raraunga \( B \).
– Ko te tūponotanga o te tūponotanga o te tirotiro i ngā raraunga ko te tūponotanga o te tirotiro i ngā raraunga ko te whakapae ko te whakapae ko te A. (P(B|A))
– Ko te \( P(A) \) te tūponotanga o mua: te whakapono tuatahi mō te tūponotanga o \( A \) i mua i te tirotiro i ngā raraunga.
– Ko te tūponotanga taha (te taunakitanga rānei) a \( P(B) \): te tūponotanga katoa o te tirotiro i ngā raraunga \( B \) i raro i ngā whakapae katoa.
Mā tēnei ariā ka whakaratohia he tikanga pūnaha mō te whakahou i te tūponotanga o tētahi whakapae i runga i te māramatanga o ngā taunakitanga hou. He tino kaha te āhua auau o te whakatau Bayesian, nā te mea ka whakatikatika tonu i ngā matapae me ngā whakapono mā te kohikohi raraunga.
Ngā mea o mua, ngā mea tūpono, me ngā mea o muri
Hei mārama ki ngā tatauranga Bayesian, me mārama hoki ki ōna wāhanga matua: te tūponotanga, te tūponotanga, me te muri.
1. Te Tūponotanga o Mua (P(A)): E whakaatu ana i ngā whakapono tuatahi mō tētahi whakapae i mua i te whakaarohia o tētahi taunakitanga. Ka taea te whakatakoto i te tūponotanga i runga i ngā raraunga hītori, i ngā whakaaro o ngā tohunga, i tētahi atu puna mōhiotanga o mua rānei. Ka ine i tā tātou e whakapono ana mō tētahi huihuinga, mō tētahi tawhā rānei i mua i te kitenga i ngā raraunga o nāianei.
2. Tūponotanga (P(B|A)): E whakaatu ana i te tūponotanga o ngā raraunga kua kitea i raro i tētahi whakapae motuhake. E hopu ana i te pai o te whakamārama a te whakapae i ngā raraunga, ā, he mea nui hoki ki te whakahou i ngā whakapono. Ko te mahi tūponotanga te mea nui ki ngā tikanga Bayesian me ngā tikanga auau.
3. Tūponotanga o Muri (P(A|B)): E whakaatu ana i te whakapono hou mō te whakapae i muri i te whakaaro ki ngā taunakitanga. Ka whakakotahi te muri i ngā mōhiotanga o mua me ngā raraunga hou, ka tukuna he tūponotanga kua whakahoutia ka taea te whakamahi mō te whakatau me te matapae.
Ngā Bayes Empirical me ngā Tauira Hierarchical
Ka horapa noa ngā tatauranga Bayesian ki ngā tauira uaua, pērā i ngā tauira hierarki me ngā tikanga Bayes empirical. Ka taea e ngā tauira hierarki, e mōhiotia ana ko ngā tauira maha-taumata, te whakatauira i ngā raraunga me ngā taumata rerekētanga maha. Hei tauira, i roto i tētahi rangahau hauora, ka taea te whakapūmau i ngā raraunga o ngā tūroro i roto i ngā hōhipera, ka whakapūmauhia anō hoki i roto i ngā rohe. Ka whakaarohia e ngā tauira hierarki ēnei momo whakawhirinakitanga, ā, ka whakarato i ngā matapae tika ake mā te tohatoha i ngā mōhiohio puta noa i ngā taumata.
Ko ngā tikanga Empirical Bayes ia, ka whakatau tata i te tohatoha o mua mai i ngā raraunga tonu. He tino whai hua tēnei huarahi ina he iti noa ngā mōhiohio o mua. Ka whakakotahi ngā tikanga Empirical Bayes i ngā mātāpono o ngā tatauranga auau me ngā tatauranga Bayesian, ka whakarato i tētahi otinga whaihua mō ngā raruraru o te ao tūturu.
Te Whakatau Bayesian me ngā Tikanga Tātari
I mua, i pāngia ngā tikanga Bayesian e ngā wero rorohiko, nā te uaua o te tatau i ngā tohatoha o muri, inā koa i ngā wāhi ahu-rahi. Heoi, nā te taenga mai o ngā tikanga rorohiko hou me te aranga ake o ngā pūmanawa Bayesian kua hurihia te whenua.
1. Markov Chain Monte Carlo (MCMC): He taputapu kaha ngā tikanga MCMC, pērā i te pūnaha Metropolis-Hastings me te tauira Gibbs, mō te whakatau tata i muri. Ka whakaputahia e ēnei pūnaha ngā tauira mai i te tohatoha muri, e āhei ai te whakatau tata me te tirohanga.
2. Whakatau Rerekētanga: Ka whakatata te whakatau rerekētanga ki te tohatoha o muri mā te arotau i tētahi tohatoha māmā ake kia tata rawa atu ki te tuara tūturu. He tere ake i te MCMC engari kāore pea i te tino tika.
3. Pūmanawa Bayesian: Kua whakawāteahia e ngā taputapu pēnei i a Stan, JAGS, me PyMC3 te urunga whānui ki ngā tikanga Bayesian. He ngāwari ki te whakamahi me ngā rauropi pakari hoki ēnei tūāpapa, ā, e wātea ana te whakatau Bayesian ki ngā kairangahau me ngā kaimahi.
Ngā Whakamahinga o ngā Tatauranga Bayesian
Nā te ngāwari me te pakari o ngā tatauranga Bayesian kua whakamahia whānuitia ki ngā momo mara:
1. Rongoā: Ka whakamahia ngā tikanga Bayesian mō ngā whakamātautau haumanu, ka taea ai te whakahou tonu i ngā mōhiotanga o mua mō te whai huatanga o te rongoā me ngā putanga o te tūroro, ka hua ake he hoahoa whakamātautau matatika me te whai hua ake.
2. Ōhanga: Mā te ohanga Bayesian ka taea te whakauru i ngā whakapono o mua mō ngā tauira me ngā tawhā ōhanga, ka whakaratohia he matapae pakari ake me ngā aromatawai kaupapa here.
3. Te Ako Mīhini: Ko ngā tikanga Bayesian te pou tautoko mō ētahi rauropi ako mīhini, tae atu ki ngā whatunga Bayesian, ngā tukanga Gaussian, me ngā kaiwhakamāori aunoa rerekētanga. Mā ēnei tikanga ka taea te whakamārama ake i ngā tauira me te ine i te koretake o te kaupapa.
4. Pūtaiao Taiao: I roto i te whakatauira āhuarangi, ka taea e ngā huarahi Bayesian te whakauru i ngā momo puna raraunga me te ine i ngā āwangawanga i roto i ngā matapae mō ngā āhuatanga āhuarangi ā muri ake nei.
5. Ira: Ka whakamahia ngā tikanga Bayesian hei hanga tauira e whakamārama ana i ngā whanaungatanga uaua i waenga i ngā ira me ngā āhuatanga, hei ārahi i ngā rangahau i roto i te tukunga iho, te koiora whanaketanga, me te rongoā whaiaro.
Ngā Painga o ngā Tatauranga Bayesian
He maha ngā painga o ngā tatauranga Bayesian i ngā tikanga tuku iho o te auau:
1. Te Whakaurunga o ngā Mātauranga o Mua: Mā ngā tikanga Bayesian ka taea te whakauru i ngā mātauranga o mua, ka hua ake he whakatau whai mōhiotanga, he whakatau e tika ana mō te horopaki.
2. Te Ako Tonu: He mea raupapa te whakatau Bayesian, he mea pai mō te whakahou i ngā whakapono ina puta mai ngā raraunga hou. He tino whai hua tēnei i roto i ngā mara hihiri pēnei i te pūtea me te aroturuki mate.
3. Te Whakamārama: He māmā ake te whakamārama i ngā tauākī tūponotanga i roto i ngā tatauranga Bayesian. Hei tauira, he mārama ake te kī "e 95% te tūponotanga kei roto i tētahi wā motuhake tētahi tawhā" i ngā wā whakawhirinaki auau.
4. Ngāwari: Ka taea e ngā tikanga Bayesian te whakahaere i ngā tauira uaua me ngā hanganga hierarki i runga ake i te taiao i ngā tikanga tuku iho, ka taea ai te whakaatu i ngā raruraru o te ao tūturu.
Opaniraa
He anga kaha ngā tatauranga Bayesian mō te whakatau me te whakatau i raro i te koretake. Mā te whakakotahi i ngā mōhiotanga o mua me ngā raraunga whaimana mā roto i te Ariā a Bayes, ka tukuna he huarahi honohono ki te whakahou i ngā whakapono me te whakatakoto matapae. Ahakoa ngā wero rorohiko, kua ngāwari ake te uru atu o ngā tikanga Bayesian ki ngā whanaketanga o ngā rauropi me ngā pūmanawa, ā, kua whakatairangahia te whakamahinga puta noa i ngā momo marautanga. I te whanaketanga tonu o te mara o te pūtaiao raraunga, kāore e kore ka whai wāhi nui te tauira Bayesian ki te hanga i te heke mai o te tātari tatauranga me tua atu.
