, ▁but ▁they ▁usually ▁conver ge ▁faster . ▁ ▁Ex amples ▁ ▁Random ▁walk ▁▁▁ ▁Metropol is – H ast ings ▁algorithm : ▁This ▁method ▁generates ▁a ▁Mark ov ▁chain ▁using ▁a ▁proposal ▁density ▁for ▁new ▁steps ▁and ▁a ▁method ▁for ▁reject ing ▁some ▁of ▁the ▁proposed ▁moves . ▁It ▁is ▁actually ▁a ▁general ▁framework ▁which ▁includes ▁as ▁special ▁cases ▁the ▁very ▁first ▁and ▁simpler ▁MC MC ▁( Met ropol is ▁algorithm ) ▁and ▁many ▁more ▁recent ▁alternatives ▁listed ▁below . ▁Gib bs ▁sampling : ▁This ▁method ▁requires ▁all ▁the ▁conditional ▁distributions ▁of ▁the ▁target ▁distribution ▁to ▁be ▁sample d ▁exactly . ▁When ▁drawing ▁from ▁the ▁full - cond itional ▁distributions ▁is ▁not ▁straightforward ▁other ▁sam pl ers - with in - G ib bs ▁are ▁used ▁( e . g ., ▁see ▁). ▁Gib bs ▁sampling ▁is ▁popular ▁partly ▁because ▁it ▁does ▁not ▁require ▁any ▁' t uning '. ▁ ▁Metropol is - ad just ed ▁L ange vin ▁algorithm ▁and ▁other ▁methods ▁that ▁rely ▁on ▁the ▁gradient ▁( and ▁possibly ▁second ▁derivative ) ▁of ▁the ▁log ▁target ▁density ▁to ▁propose ▁steps ▁that ▁are ▁more ▁likely ▁to ▁be ▁in ▁the ▁direction ▁of ▁higher ▁probability ▁density . ▁Pse udo - m arg inal ▁Metropol is – H ast ings : ▁This ▁method ▁rep laces ▁the ▁evaluation ▁of ▁the ▁density ▁of ▁the ▁target ▁distribution ▁with ▁an ▁un bi ased ▁estimate ▁and ▁is ▁useful ▁when ▁the ▁target ▁density ▁is ▁not ▁available ▁analyt ically , ▁e . g . ▁lat ent ▁variable ▁models . ▁ ▁S