ressions and is denoted by ܢ

⋃ሼܠ, ܡሽ. A tight Gaussian cluster

noted by ܢ^ା. A tight cluster box is defined as above, i.e., ߱ൌ

ߤ൅2ߪොሿ for 95% of a Gaussian confidence interval. A candidate

t ܢ^ି is composed of all expressions which are not included in the

ter set ܢ^ା and is denoted by

ܢ^ିൌሼݖ௜

ି∈ܢ|ݖ௜

ି∉߱ሽ

(6.18)

d on the initial tight cluster ܢ^ା and an initial candidate outlier set

adaptive learning process is implemented using the Bayesian

mechanism [Yang and Yang, 2013]. The likelihood function of

sian tight cluster is defined as below, where i is an identity vector

ߪ^ିଶ,

ࣦሺܢ^ା|ߤ, ߚሻൌ^ඨߚ

2ߨ^{exp ൬െ1}

2 ^{ߚሺܢାെߤܑሻଶ൰}

(6.19)

his Gaussian likelihood function, one a priori structure for the

ariance ߚ is defined as an inverse Gamma

IGሺߚ|ܽ, ܾሻൌ^ܾ௔

Γሺܽሻ^{ߚିሺଵା௔ሻexp ൬ܾ}

ߚ^൰

(6.20)

or for the mean ߤ is defined as a Gaussian function,

ܩሺߤ|ߤ଴, ߪ଴

ଶሻൌ

1

ඥ2ߨߪ଴

ଶ^{exp ቆെ}

ሺߤെߤ଴ሻ^ଶ

2ߪ଴

ଶ

ቇ

(6.21)

og-posterior of the likelihood combined with priors leads to the

g model format, where the model parameter set is ߠൌሺߤ, ߚሻ and

-parameter set is ߙൌሺߤ଴, ߪ଴

ଶ, ܽ, ܾሻ,

ogܲሺߠ|ݖ^ା, ߙሻ∝logࣦሺܢ^ା|ߤ, ߚሻ൅logIGሺߚ|ܽ, ܾሻ

൅logܩሺߤ|ߤ଴, ߪ଴

ଶሻ

(6.22)

above equation, the log-likelihood is simplified as below,