og-prior ߚ of is simplified as below,
logIGሺߚ|ܽ, ܾሻ∝ܽlogܾሺܽ1ሻlogߚെܾߚ
(6.24)
og-prior of ߤ is simplified as below,
logܩሺߤ|ߤ, ߪ
ଶሻ∝െ1
2 logߪ
ଶെ
ሺߤെߤሻଶ
2ߪ
ଶ
(6.25)
optimisation follows the procedure of maximising a posteriori
2006]. The process is implemented in two steps, i.e., the
on step and the maximisation step. In the expectation step, the
is calculated based on both the model parameters and the hyper-
rs. In the maximisation step, the model parameters and the hyper-
rs are updated based on the evaluated posterior. The update of ߤ
below [Yang and Yang, 2013],
ߤൌߚ∑ݖ
ା
ߚߤ
ߚ݊ߚ
(6.26)
pdate rule for ߚ is shown below,
ߚൌ
݊2ܽ2
∑൫ݖ
ାെߤ൯
ଶ2ܾ
(6.27)
pdate rule for ߚ is shown below,
ߚൌ
ܽ1
ሺߤെߤሻଶ/2 ܾ
(6.28)
d on the analysis above, a new t statistic is defined as below, where
is the first candidate outlier in ܢି or the one which is most close
ht cluster box,
ݐൌݖ
ିെߤ
ߪ
(6.29)