lice ▁sampling : ▁This ▁method ▁depends ▁on ▁the ▁principle ▁that ▁one ▁can ▁sample ▁from ▁a ▁distribution ▁by ▁sampling ▁uniformly ▁from ▁the ▁region ▁under ▁the ▁plot ▁of ▁its ▁density ▁function . ▁ ▁It ▁altern ates ▁uniform ▁sampling ▁in ▁the ▁vertical ▁direction ▁with ▁uniform ▁sampling ▁from ▁the ▁horizontal ▁' slice ' ▁defined ▁by ▁the ▁current ▁vertical ▁position . ▁ ▁Multiple - try ▁Metropol is : ▁This ▁method ▁is ▁a ▁variation ▁of ▁the ▁Metropol is – H ast ings ▁algorithm ▁that ▁allows ▁multiple ▁tri als ▁at ▁each ▁point . ▁By ▁making ▁it ▁possible ▁to ▁take ▁larger ▁steps ▁at ▁each ▁iteration , ▁it ▁helps ▁address ▁the ▁cur se ▁of ▁dimensional ity . ▁ ▁Re vers ible - j ump : ▁This ▁method ▁is ▁a ▁variant ▁of ▁the ▁Metropol is – H ast ings ▁algorithm ▁that ▁allows ▁propos als ▁that ▁change ▁the ▁dimensional ity ▁of ▁the ▁space . ▁ ▁Mark ov ▁chain ▁Monte ▁Carlo ▁methods ▁that ▁change ▁dimensional ity ▁have ▁long ▁been ▁used ▁in ▁statistical ▁physics ▁applications , ▁where ▁for ▁some ▁problems ▁a ▁distribution ▁that ▁is ▁a ▁grand ▁canonical ▁ensemble ▁is ▁used ▁( e . g ., ▁when ▁the ▁number ▁of ▁mole cules ▁in ▁a ▁box ▁is ▁variable ). ▁ ▁But ▁the ▁revers ible - j ump ▁variant ▁is ▁useful ▁when ▁doing ▁Mark ov ▁chain ▁Monte ▁Carlo ▁or ▁Gib bs ▁sampling ▁over ▁non param et ric ▁Bay esian ▁models ▁such ▁as ▁those ▁involving ▁the ▁Dir ich let ▁process ▁or ▁Chinese ▁restaurant ▁process , ▁where ▁the ▁number ▁of ▁mixing ▁components / cl ust ers / etc . ▁is ▁automatically