▁example ▁in ▁Bay esian ▁statistics , ▁computational ▁physics , ▁computational ▁bi ology ▁and ▁computational ▁lingu istics . ▁ ▁In ▁Bay esian ▁statistics , ▁the ▁recent ▁development ▁of ▁MC MC ▁methods ▁has ▁made ▁it ▁possible ▁to ▁compute ▁large ▁hier arch ical ▁models ▁that ▁require ▁integr ations ▁over ▁hundreds ▁to ▁thousands ▁of ▁unknown ▁parameters . ▁ ▁In ▁rare ▁event ▁sampling , ▁they ▁are ▁also ▁used ▁for ▁generating ▁samples ▁that ▁gradually ▁populate ▁the ▁rare ▁failure ▁region . ▁ ▁In ▁crypt oc urrency , ▁MC MC ▁has ▁been ▁used ▁for ▁generating ▁forec asts ▁based ▁on ▁historical ▁price ▁data . ▁ ▁General ▁explanation ▁▁ ▁Mark ov ▁chain ▁Monte ▁Carlo ▁methods ▁create ▁samples ▁from ▁a ▁continuous ▁random ▁variable , ▁with ▁probability ▁density ▁proportional ▁to ▁a ▁known ▁function . ▁These ▁samples ▁can ▁be ▁used ▁to ▁evaluate ▁an ▁integral ▁over ▁that ▁variable , ▁as ▁its ▁expected ▁value ▁or ▁variance . ▁ ▁Pract ically , ▁an ▁ensemble ▁of ▁ch ains ▁is ▁generally ▁developed , ▁starting ▁from ▁a ▁set ▁of ▁points ▁arbitr arily ▁chosen ▁and ▁sufficiently ▁distant ▁from ▁each ▁other . ▁These ▁ch ains ▁are ▁st ochastic ▁processes ▁of ▁" walk ers " ▁which ▁move ▁around ▁randomly ▁according ▁to ▁an ▁algorithm ▁that ▁looks ▁for ▁places ▁with ▁a ▁reason ably ▁high ▁contribution ▁to ▁the ▁integral ▁to ▁move ▁into ▁next , ▁assigning ▁them ▁higher ▁prob abilities . ▁ ▁Random ▁walk ▁Monte ▁Carlo ▁methods ▁are ▁a ▁kind ▁of ▁random ▁simulation ▁or ▁Monte ▁Carlo ▁method . ▁However , ▁whereas ▁the ▁random ▁samples ▁of ▁the ▁integr and ▁used ▁in ▁a ▁conventional ▁Monte ▁Carlo ▁integration ▁are ▁statist ically ▁independent