Tauira o ngā Pātai Kōrero mō te Atamira Metropolis
I roto i te horopaki o ngā whakatauira Monte Carlo, he mea nui te wāhanga Metropolis i roto i te hangarau tatauranga me ētahi atu mara. I tēnei wāhanga, ka matapakihia e mātou te tikanga Metropolis-Hastings, he pūnaha e whakamahia ana hei tauira mai i ngā tohatoha tūponotanga matatini. Mā te mārama ki ngā mahi o tēnei pūnaha, ka taea e tātou te mahi whakatauira tika ake, whai hua ake hoki.
He Kupu Whakataki ki te Pūmanawa Metropolis
I whakaurua te pūnaha Metropolis e Nicholas Metropolis me āna hoa mahi i te tau 1953. E whakamahia ana tēnei tikanga hei whakatauira me te whaihanga i te āhua o ngā pūnaha ā-tinana, inā koa ko ērā e whai wāhi ana ki ngā matūriki maha pērā i te hau, te wai rānei. Ko te putanga hou o tēnei pūnaha, ko Metropolis-Hastings, he whakawhanuitanga e āhei ai te tango tauira mai i tētahi tohatoha ūnga kāore i te whakatauritea.
Ngā Hipanga i roto i te Pūnaha Metropolis
Hei mārama ki te mahi a te pūnaha Metropolis, he mea nui kia mōhio koe ki ngā kaupae:
1. Te Tīmatanga: Tīmata mā te tīpako matapōkere i tētahi otinga tīmatanga mai i te wāhi otinga, i te tohatoha tīmatanga rānei. Hei tauira, ka tīmata tātou me tētahi āhuatanga pāmahana, tūranga matūriki rānei.
2. Te Whakatakoto i tētahi Hipanga Hou: Whakatakotoria he āhua hou (otinga hou) mā te hanga i tētahi huringa iti ki te āhua o nāianei. E kiia ana tēnei ko te taahiraa "whakatakoto". I te nuinga o te wā ka tangohia tēnei huringa mai i tētahi tohatoha ōrite, pērā i te tohatoha Gaussian.
3. Te Tatau i te Ōwehenga Whakaae: Tātaihia te ōwehenga whakaae, e whakatau ana mēnā ka whakaaetia, ka whakahē rānei tātou i tētahi nekehanga kua whakaarohia. Ko tēnei ōwehenga te ōwehenga o te tūponotanga o te āhua hou ki te āhua o nāianei. I roto i te tuhi pāngarau, ka hoatu tēnei ōwehenga e:
\[
A = \min\left(1, \frac{P(\text{new})}{P(\text{current})}\right)
\]
ko \( P \) te tūponotanga o tētahi āhua motuhake.
4. Whakataunga Mā te Whakamahi i te Ōwehenga Whakaae: Whakatauritea te ōwehenga whakaae ki tētahi uara matapōkere i tangohia mai i tētahi tohatoha ōrite i waenga i te 0 me te 1. Mena he nui ake te ōwehenga whakaae i te uara matapōkere, whakaaetia te nekehanga hou; ki te kore, whakakahoretia, ā, noho tonu ki te āhua o nāianei.
5. Whakahoutanga: Whakahoutia ngā taahiraa 2 ki te 4 mō te maha o ngā whakahoutanga e hiahiatia ana, kia tae rā anō te pūnaha ki te taurite.
Ngā Pātai Tauira me te Kōrero
Me matapaki tātou i ētahi tauira pātai hei mārama ake i te wāhanga o Metropolis.
Tauira Pātai 1
Pātai: Kei a koe tētahi matūriki i te taha kotahi o te tūranga \( x \) e pāngia ana e te mahi pūngao pūmanawa \( U(x) = x^2 \). Whakamahia te pūnaha Metropolis hei whakatauira i te tohatoha o ngā tūranga matūriki.
Kōrero:
1. Whakatūnga: Tīmata mai i te tūranga \( x = 0 \).
2. Whakaarohia he Nekehanga Hou: Whakaarohia he tūranga hou \( x' = x + \Delta x \), me \( \Delta x \) i tangohia mai i te tohatoha Gaussian me te kore toharite.
3. Tātaitanga o te ōwehenga pūngao: Tātaihia te ōwehenga pūngao:
\[
Teihana U = U(x') – U(x) = x'^2 – x^2
\]
Nō reira, ko te ōwehenga whakaae ko:
\[
A = \min\left(1, e^{-\Delta U}\right)
\]
4. Whakatau: Mena he nui ake a \( A \) i te tau matapōkere i waenga i te 0 me te 1, whakaaetia \( x' \); ki te kore, noho tonu ki te tūranga \( x \).
5. Whakahoutanga: Whakahokia tēnei tukanga, hei tauira, kia 10,000 ngā hikoinga.
Ko te tohatoha tūranga ka puta mai ka whai i te tohatoha Gaussian me te kore toharite, ā, he rite whakamuri te rerekētanga ki te pūmanawa, ā, i tēnei wā, ka hua ake he tohatoha i hangaia e te mahi pūngao pūmanawa.
Tauira Pātai 2
Pātai: Whakamahia te pūnaha Metropolis hei whakauru i te whakatau mahi Bayesian. Me kī tātou e hiahia ana tātou ki te whakauru i tētahi pari māmā ki roto i tētahi huinga raraunga mā te whakamahi i te whakatautautanga rārangi me te MCMC.
Kōrero:
1. Whakatīmatatanga: Tautuhia ngā tawhā tauira tīmatanga \( \beta = (m, c) \).
2. Te Whakatakoto i tētahi Hipanga Hou: Whakatakotoria he tawhā hou mō te tohatoha tono noa maha-taurangi. Hei tauira, whakamahia he tohatoha Gaussian mō ngā taurangi \( m \) me \( c \).
3. Ōwehenga Whakaae: Tātaihia te ōwehenga whakaae mā te:
\[
A = \min\left(1, \frac{L(m', c'| \text{data})P(m', c')}{L(m, c| \text{data})P(m, c)}\right)
\]
Ko \( L \) te tūponotanga, ā, ko \( P \) te mua o te tawhā.
4. Whakatau: Whakatauritea te ōwehenga ki te uara matapōkere o te 0 ki te 1 hei whakaae, hei whakakore rānei i te tono.
5. Whakahoutanga: Whakahaerehia te whakatauira me ngā whakahounga e ranea ana kia tutuki rā anō te huihuinga.
Mā tēnei huarahi, ka taea e tātou te whiwhi i ngā tohatoha o muri mō ngā tawhā whakatauira, ka hoatu he huarahi ki a tātou ki te whakatau me te whakamārama i ngā whanaungatanga i roto i ngā raraunga.
Whakamutunga
Mā te wāhanga Metropolis i roto i ngā whakatauira Monte Carlo ka taea e tātou te tango tauira mai i ngā tohatoha whāinga uaua, ā, koinei te pūtake mō te tikanga Metropolis-Hastings. Mā te whakamahi i tēnei tikanga ki ngā momo mara, ka taea e tātou te whakatutuki i te whakatauira tika ake me te māramatanga taipitopito ake o te pūnaha. I roto i ngā tono mai i te ahupūngao me te koiora ki te pūtaiao rorohiko me ngā tatauranga, ka tukuna e tēnei rauropi he otinga huatau me te whai hua ki ngā raruraru uaua.
