▁infer red ▁from ▁the ▁data . ▁ ▁Hamiltonian ▁( or ▁Hy brid ) ▁Monte ▁Carlo ▁( H MC ): ▁T ries ▁to ▁avoid ▁random ▁walk ▁behaviour ▁by ▁introdu cing ▁an ▁auxili ary ▁momentum ▁vector ▁and ▁implementing ▁Hamiltonian ▁dynamics , ▁so ▁the ▁potential ▁energy ▁function ▁is ▁the ▁target ▁density . ▁The ▁momentum ▁samples ▁are ▁disc arded ▁after ▁sampling . ▁The ▁end ▁result ▁of ▁Hy brid ▁Monte ▁Carlo ▁is ▁that ▁propos als ▁move ▁across ▁the ▁sample ▁space ▁in ▁larger ▁steps ; ▁they ▁are ▁therefore ▁less ▁correl ated ▁and ▁conver ge ▁to ▁the ▁target ▁distribution ▁more ▁rapidly . ▁ ▁Training - based ▁ ▁Another ▁approach ▁is ▁to ▁use ▁the ▁previous ▁steps ▁to ▁generate ▁the ▁next ▁candidate . ▁This ▁training - based ▁algorithm ▁is ▁able ▁to ▁acceler ate ▁MC MC ▁by ▁an ▁order ▁of ▁magnitude . ▁ ▁Inter act ing ▁MC MC ▁method ologies ▁are ▁a ▁class ▁of ▁mean ▁field ▁particle ▁methods ▁for ▁obtain ing ▁random ▁samples ▁from ▁a ▁sequence ▁of ▁probability ▁distributions ▁with ▁an ▁increasing ▁level ▁of ▁sampling ▁complexity . ▁These ▁probabil istic ▁models ▁include ▁path ▁space ▁state ▁models ▁with ▁increasing ▁time ▁horizon , ▁posterior ▁distributions ▁w . r . t . ▁sequence ▁of ▁partial ▁observations , ▁increasing ▁constraint ▁level ▁sets ▁for ▁conditional ▁distributions , ▁decre asing ▁temperature ▁sched ules ▁associated ▁with ▁some ▁Bol tz mann - G ib bs ▁distributions , ▁and ▁many ▁others . ▁In ▁principle , ▁any ▁Mark ov ▁chain ▁Monte ▁Carlo ▁sam pler ▁can ▁be ▁turned ▁into ▁an ▁interact ing ▁Mark ov ▁chain ▁Monte ▁Carlo ▁sam pler . ▁These ▁interact ing ▁Mark