݂۰|۳ሺ۰ሻ∝݂۳|۰ሺ۳ሻ݂۰ሺΘሻ݂|ሺΘሻ
(5.36)
osterior for modelling replicated spectra is defined as below,
ሺ۰ሻ∝൫ߪ,ௌ
ଶ൯
ିఠೄ൫ߪ,ி
ଶ
൯
ିఠಷ
ெ
ୀଵ
exp ൭െ߭
ெ
ୀଵ
൱
ݓ
ఈೢିଵ
ெ
expሺെߚ௪ݓሻ
ୀଵ
(5.37)
above equation, ߭ is defined as below,
߭ൌ܍
௧Γ܍
2ߪ,ி
ଶ
܌
௧܌
2ߪ,ௌ
ଶ
ߚ,ி
ߪ,ி
ଶ
ߚ,ௌ
ߪ,ௌ
ଶ
(5.38)
oise threshold variable w can be estimated by maximising the
and is shown below,
ݓൌ
ߚ௪1
2ܯߢߪ,ி
ିଶ܍
௧۶܍
ߙ௪െ1
(5.39)
above equation, H is an entropy matrix and is defined as
۶ ൌdiag൛ሾݎሺ1 െݎሻሿୀଵ
ேൟ
(5.40)
ext issue is the derivative of the error term ݐሺݏെܾሻଶ. Because
a sigmoid term in the expression of ݐ, the derivative is slightly
ted. Therefore, a linear approximation is used in BWH, which is
low,
ݐሺݏെܾሻݎሺ1 െݎሻሺݏെܾሻଶൎݐሺݏെܾሻ
(5.41)
e 5.18 shows the hierarchical structure of BWH. The Bayesian
r-Henderson package can request to the author via an email.
e 5.19 shows an alignment of a peak across multiple replicates.
tra of the first peak from multiple replicates in a replicated spectra