, ▁those ▁used ▁in ▁MC MC ▁are ▁aut oc or related . ▁Cor rel ations ▁of ▁samples ▁introdu ces ▁the ▁need ▁to ▁use ▁the ▁Mark ov ▁chain ▁central ▁limit ▁theorem ▁when ▁estim ating ▁the ▁error ▁of ▁mean ▁values . ▁ ▁These ▁algorithms ▁create ▁Mark ov ▁ch ains ▁such ▁that ▁they ▁have ▁an ▁equilibrium ▁distribution ▁which ▁is ▁proportional ▁to ▁the ▁function ▁given . ▁ ▁Red uc ing ▁correlation ▁While ▁MC MC ▁methods ▁were ▁created ▁to ▁address ▁multi - dimensional ▁problems ▁better ▁than ▁generic ▁Monte ▁Carlo ▁algorithms , ▁when ▁the ▁number ▁of ▁dimensions ▁r ises ▁they ▁too ▁tend ▁to ▁suffer ▁the ▁cur se ▁of ▁dimensional ity : ▁regions ▁of ▁higher ▁probability ▁tend ▁to ▁stretch ▁and ▁get ▁lost ▁in ▁an ▁increasing ▁volume ▁of ▁space ▁that ▁cont ributes ▁little ▁to ▁the ▁integral . ▁One ▁way ▁to ▁address ▁this ▁problem ▁could ▁be ▁short ening ▁the ▁steps ▁of ▁the ▁walk er , ▁so ▁that ▁it ▁doesn ' t ▁continu ously ▁try ▁to ▁exit ▁the ▁highest ▁probability ▁region , ▁though ▁this ▁way ▁the ▁process ▁would ▁be ▁highly ▁aut oc or related ▁and ▁expensive ▁( i . e . ▁many ▁steps ▁would ▁be ▁required ▁for ▁an ▁accurate ▁result ). ▁More ▁s oph istic ated ▁methods ▁such ▁as ▁Hamiltonian ▁Monte ▁Carlo ▁and ▁the ▁Wang ▁and ▁Land au ▁algorithm ▁use ▁various ▁ways ▁of ▁reducing ▁this ▁aut oc or relation , ▁while ▁man aging ▁to ▁keep ▁the ▁process ▁in ▁the ▁regions ▁that ▁give ▁a ▁higher ▁contribution ▁to ▁the ▁integral . ▁These ▁algorithms ▁usually ▁rely ▁on ▁a ▁more ▁complicated ▁theory ▁and ▁are ▁harder ▁to ▁implement