ic ▁uncertainty ▁and ▁physical ▁uncertainty ▁than ▁Bay esian ▁theory . ▁▁ ▁For ▁example , ▁the ▁height ▁of ▁an ▁un ob ser ved ▁person ▁from ▁a ▁population ▁may ▁have ▁a ▁Gaussian ▁belief ▁distribution ▁with ▁a ▁high ▁variance , ▁but ▁Bay esian ▁theory ▁obtain s ▁the ▁same ▁distribution ▁in ▁the ▁case ▁where ▁all ▁people ▁are ▁the ▁same ▁height ▁but ▁little ▁data ▁is ▁available ▁about ▁what ▁that ▁height ▁is , ▁as ▁in ▁the ▁case ▁where ▁there ▁is ▁a ▁wide ▁range ▁of ▁phys ically ▁different ▁height s ▁in ▁the ▁population . ▁▁ ▁Standard ▁Bay esian ▁theory ▁may ▁lead ▁to ▁sub opt imal ▁dec isions ▁if ▁this ▁difference ▁is ▁not ▁account ed ▁for ▁using ▁second - order ▁probability ▁and ▁mach in ery ▁to ▁estimate ▁util ities ▁of ▁information - g ather ing ▁actions . ▁ ▁It ▁has ▁also ▁been ▁argued ▁that ▁D S ▁theory ▁is ▁not ▁a ▁general isation ▁of ▁Bay esian ▁theory . ▁ ▁Bay esian ▁approximation ▁The ▁Bay esian ▁approximation ▁[ V oor bra ak , ▁ 1 9 8 9 ) ▁reduces ▁a ▁given ▁b pa ▁ ▁to ▁a ▁( dis crete ) ▁probability ▁distribution , ▁i . e . ▁only ▁singleton ▁subsets ▁of ▁the ▁frame ▁of ▁disc ern ment ▁are ▁allowed ▁to ▁be ▁foc al ▁elements ▁of ▁the ▁approxim ated ▁version ▁ ▁Mark up <0x09> R enders ▁as ▁ ▁of ▁: ▁ ▁It ' s ▁useful ▁for ▁those ▁who ▁are ▁only ▁interested ▁in ▁the ▁single ▁state ▁hypothesis . ▁ ▁We ▁can ▁perform ▁it ▁in ▁the ▁' light ' ▁example . ▁ ▁Crit ic ism