Muenzaniso weMibvunzo yeKukurukurirana yeMetropolis Stage
Mukutaura nezveMonte Carlo simulations, danho reMetropolis inzira yakakosha mu statistical mechanics nedzimwe nzvimbo. Muchikamu chino, tinonyanya kutaura nezve Metropolis-Hastings method, nzira inoshandiswa kuenzanisa kubva mukugoverwa kwakaoma kweprobability. Nekunzwisisa matanho ari mu algorithm iyi, tinogona kuita simulations dzakarurama uye dzinoshanda.
Nhanganyaya kuMetropolis Algorithm
Nzira yeMetropolis yakatangwa naNicholas Metropolis nevamwe vake muna 1953. Nzira iyi inoshandiswa kutevedzera mamiriro ezvinhu emuviri, kunyanya ayo ane zvidimbu zvakawanda zvakaita semagasi kana mvura. Shanduro yemazuva ano yeiyi nzira, Metropolis-Hastings, inzira yekusanganisa sampuli kubva pakugoverwa kwezvinangwa zvisiri zvepamutemo.
Matanho muMetropolis Algorithm
Kuti unzwisise mashandiro anoita Metropolis algorithm, zvakakosha kuti uzive matanho anotevera:
1. Kutanga: Tanga nekusarudza mhinduro yekutanga kubva munzvimbo yemhinduro kana kugoverwa kwekutanga. Semuenzaniso, tinotanga nemamiriro ekupisa kana nzvimbo yezvikamu.
2. Kupa Danho Idzva: Kupa mamiriro matsva (mhinduro itsva) nekuita shanduko diki kune mamiriro aripo iye zvino. Izvi zvinowanzonzi danho rekuti "chikumbiro". Shanduko iyi inowanzotorwa kubva mukugoverwa kwakaenzana, senge kugoverwa kweGaussian.
3. Kuverenga Chiyero Chekugamuchira: Verenga chiyero chekugamuchira, icho chinoona kana tichigamuchira kana kuramba danho riri kutaurwa. Chiyero ichi chiyero chemukana wemamiriro matsva kune mamiriro aripo. Mukunyora kwemasvomhu, chiyero ichi chinopiwa na:
\[
A = \min\left(1, \frac{P(\text{new})}{P(\text{current})}\right)
\]
apo \( P \) ndiyo mukana wekuti mamiriro acho aite chimwe chinhu.
4. Sarudzo Uchishandisa Chiyero Chekugamuchira: Enzanisa chiyero chekugamuchira nechiyero chisina kurongeka chinotorwa kubva mukugoverwa kwakafanana pakati pe0 ne1. Kana chiyero chekugamuchira chiri chikuru pane chiyero chisina kurongeka, gamuchira danho idzva; kana zvisina kudaro, ramba uye ramba uri mumamiriro azvino.
5. Kudzokorora: Dzokorora matanho 2 kusvika 4 kuti uwane nhamba yaunoda yekudzokorora kana kusvika sisitimu yasvika pakuenzana.
Mibvunzo yemuenzaniso nekukurukurirana
Ngatikurukurei mimwe mienzaniso yemibvunzo kuti tinzwisise zviri nani Metropolis stage.
Muenzaniso Mubvunzo 1
Mubvunzo: Une chidimbu chiri muchikamu chimwe chete chenzvimbo \( x \) icho chinokanganiswa nebasa resimba rinogona kushanda \( U(x) = x^2 \). Shandisa Metropolis algorithm kutevedzera kugoverwa kwenzvimbo dzechidimbu.
Kukurukurirana:
1. Kutanga: Tanga kubva panzvimbo \( x = 0 \).
2. Ronga Chifambiso Chitsva: Ronga chinzvimbo chitsva \( x' = x + \Delta x \), ne \( \Delta x \) yakatorwa kubva mukugoverwa kweGaussian neavhareji zero.
3. Kuverenga Simba Ratio: Verenga simba rehuwandu:
\[
\Delta U = U(x') – U(x) = x'^2 – x^2
\]
Saka, chiyero chekugamuchirwa ndeichi:
\[
A = \min\left(1, e^{-\Delta U}\right)
\]
4. Sarudzo: Kana \( A \) iri nhamba inopfuura isina kurongeka iri pakati pa0 na1, gamuchira \( x' \); kana zvisina kudaro, ramba uri panzvimbo \( x \).
5. Kudzokorora: Dzokorora maitiro aya nematanho zviuru gumi.
Kugoverwa kwenzvimbo kunotevera kugoverwa kweGaussian ne zero iri pakati uye musiyano uripo zvichienderana ne potential, izvo muchiitiko ichi, zvinoguma nekugoverwa kwakaumbwa nebasa re potential energy.
Muenzaniso Mubvunzo 2
Mubvunzo: Shandisa Metropolis algorithm kuti ikwane neBayesian function inference. Ngatitii tinoda kukodzera slope iri nyore mudataset tichishandisa linear regression neMCMC.
Kukurukurirana:
1. Kutanga: Gadza maparamita ekutanga emuenzaniso \( \beta = (m, c) \).
2. Kupa Danho Idzva: Kupa maparamita matsva ekugoverwa kweproposal yakajairika yemultivariate. Semuenzaniso, shandisa kugoverwa kweGaussian kune variables \( m \) uye \( c \).
3. Chiyero chekugamuchira: Verenga chiyero chekugamuchira ne:
\[
A = \min\left(1, \frac{L(m', c'| \text{data})P(m', c')}{L(m, c| \text{data})P(m, c)}\right)
\]
Apo \( L \) iri mukana, uye \( P \) iri pamberi peparamende.
4. Sarudzo: Enzanisa chiyero nemutengo usingatarisirwi we0 kusvika 1 kuti ugamuchire kana kuramba chikumbiro chacho.
5. Kudzokorora: Shandisa simulation yacho nekudzokorora kwakakwana kusvika yasvika pakubatana.
Nekushandisa nzira iyi, tinogona kuwana posterior distributions dze regression parameters, zvichitipa nzira yekufungidzira nekududzira hukama mudata.
Mhedziso
Danho reMetropolis muMonte Carlo simulations rinotibvumira kuti tikwanise kuita sampuli kubva mukugoverwa kwakaoma uye rinoshanda sehwaro hwenzira yeMetropolis-Hastings. Nekushandisa nzira iyi muzvikamu zvakasiyana-siyana, tinogona kuwana modhirowa yakarurama uye kunzwisisa kwakadzama kwehurongwa. Mumashandisirwo akasiyana kubva kufizikisi nebiology kusvika kusainzi yekombuta nenhamba, iyi algorithm inopa mhinduro dzakanaka uye dzinoshanda kumatambudziko akaoma.
