݌ሺܟ|߱ሻൌ൬^ߚ

2ߨ^൰

௄

ଶ

exp ൬െ^ߚ

2 ^ܟ௧ܟ൰

(3.58)

s

߱ሻൌ൬^ߴ

2ߨ^൰

ଵ/ଶ

exp ൬െ^ߴ

2 ^{ߙଶ൰ቀ߬}

2ߨ^ቁ

ଵ/ଶ

exp ቀെ^߬

2 ^ߚଶቁ

(3.59)

ative logarithm of ࣦ thus leads to

ൌ¹

2 ^{൜ߙሺ܁ܟെܡሻ௧ሺ܁ܟെܡሻ൅ߚܟ௧ܟ൅ߴߙଶ൅߬ߚଶ}

െܰlogα െܭlogߚെlogߴെlog߬

ൠ

(3.60)

maximum a posteriori procedure is used to estimate parameters for

BBFNN [Yang, 2005b]. The parameters are updated in a loop

initialised values for w, ߴ and ߬. The parameters ߙ and ߚ are

d at first. The estimate of ߙ is shown below, where e is an error

tween a model output vector ܡො and a target vector y,

ߙൌ^{െ܍ଶ൅√܍ସ൅8ߴܰ}

4ߴ

(3.61)

stimate of ߚ is shown below,

ߚൌ^{െܟ௧ܟ൅ඥሺܟ௧ܟሻଶ൅8߬ܭ}

4߬

(3.62)

ߙ and ߚ have been estimated, w is estimated using the following

ܟ= ߙሺߙ܁^௧܁൅ߚ۷ሻ^ିଵ܁^௧ܡ

(3.63)

wards, the hyper parameters are also updated as below,