Page 102 - Contributed Paper Session (CPS) - Volume 5

CPS1111 Jitendra Kumar et al.
symmetric and asymmetric loss function. We are not getting closed form
expressions of Bayes estimators under assumed loss function. Hence, Gibbs
sampling, an iterative procedure is used to get the approximate values of the
estimators using conditional posterior distribution and then, computed the
credible interval.

3.3 Significance Test for Merger Coefficient
This section provides testing procedure to test the impact of merger series in
model and targeting to analysis the impact on model as associate series may
be influencing the model negatively or positively. Therefore, null hypothesis is
assumed that merger coefficients are equal to zero H0: δ=0 against the
alternative hypothesis that merger has a significant impact to the observed
series H1: δ≠0. The models under hypothesis is

Under H0: Y  l   X    (12)
Under H1: Y  l   X   Z    (13)
There are several Bayesian methods to handle the problem of testing the
hypothesis. The commonly used testing strategy is Bayes factor, full Bayesian
significance test and test based on credible interval. Bayes factor is the ratio
of posterior probability under null versus alternative hypothesis.
T  c
P y | H    S  2
1
BF  1  A 2   0  (14)

10
P y | H 0  3  S 1 
where
A 1  l l ' 2 1  
  I
1
A  X ' X  I  p 1  p 2  X ' lA 1  1 l ' X
2
'
A  Z ' Z  I R  1  Z ' lA 1  1 l ' Z  Z ' X  Z ' lA 1  1 l ' X  A 2  1 Z ' X  Z ' lA 1  1 l ' X 
3
'
B  Y ' X  ' I  1   l   ' I  1  A  1 l ' X
Y
'
'
21 p 1  p 2 2 1
'
'
'
B  Y ' Z  ' I R  1   lY   ' I 2  1  A 1  1 l ' Z  B 21 A 2  1 Z ' X  Z ' lA 1  1 l ' X 
3
'
S  Y ' Y   ' I  1 1 p  p 2    ' I   2b   l   ' I 2  1  A 1  1  l   ' I 2  1  B 21 A 2  1 B

1
'
'
Y
Y
'
2
21
0
1 
S  S  ' I   B 3 ' A 3 1  B
R
0
1
3

Using the Bayes factor, we easily have taken decision regarding the acceptance
or rejection of hypothesis. For large value of BF10, we lead to rejection of null
hypothesis. With the help of BF10, posterior probability of proposed model is
also obtained. In recent time, a full Bayesian significance test (FBST) is mostly
used for testing the significance of a hypothesis or model. This test determines
in respect to null hypothesis and concluded that small value of evidence
measure support the alternative hypothesis. The evidence measure of FBST
test is described by Ev =1-  where =P (:(|Y) > (0|Y)). Another procedure
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