Posterior distribution
CJMJUJFT .BZCF ĕY σ = BOE UIFO DPOTJEFS POMZ α = , β = BOE α =
QQPTF XF BMSFBEZ IBWF B QSFMJNJOBSZ QPTUFSJPS EJTUSJCVUJPO
1S(α, β, σ)
GP
JUJFT /PX XF HFU UIF EBUB GPS B OFX JOEJWJEVBM
)J
BOE 8J
8F XBOU UP VQ
PS TP JU JODMVEFT UIJT JOEJWJEVBM 'PS BOZ DPNCJOBUJPO PG α BOE β BOE σ
UIF Q
MJUZ JT
1S(α, β, σ|)J, 8J) =
1S(8J|)J, α, β, σ) 1S(α, β, σ)
;
; JT PVS GSJFOEMZ OPSNBMJ[JOH DPOTUBOU ćF BDUJPO BT BMXBZT JT PO UPQ *O #
XF UBLF UIF QSFWJPVT QPTUFSJPS QSPCBCJMJUZ UIF QSJPS QSPCBCJMJUZ
PG UIJT DPNC
, σ) BOE NVMUJQMZ JU CZ UIF SFMBUJWF OVNCFS PG XBZT QSPCBCJMJUZ
UIBU UIJT DPNC
FT DPVME QSPEVDF UIF PCTFSWBUJPO 8J
XIJDI JT 1S(8J|)J, α, β, σ)
T UBLF XIBU XF IBWF TP GBS BOE BDUVBMMZ EP TPNF DBMDVMBUJPOT -FUT NBLF JU F
σ = BOE α = 4P UIFO XF KVTU OFFE UP DPOTJEFS EJČFSFOU QPTTJCMF WBMVF