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Ta b l e 1 . Activation probabilities and conditional activation probabilities of epistatic effects be-
tween locus l j and locus l k
l i
l j
P ( l ij | D ) P ( l ij |l i ,l j , D )
ATHCHIB2 MSAT5-9
0.070
0.243
ATHCHIB2 MSAT5-22
0.061
0.191
MSAT5-9
MSAT5-22
0.062
0.135
4.1
Sensitivity Study
To assess the impact of the restriction on the resulting inferences a simulation study
was conducted. Using the same data set and prior distributions, different analyzes were
performed by varying the restriction paramter r . Four choices of r were chosen: r =8 ,
r =10 , r =12 and r =14 . This corresponds to the following maximum model sizes,
max
= 105 , respectively.
Since the data set only has 158 observations, if r> 14 then, the degrees of freedom
associated with the maximum model would be less than 50 .
Table 2 shows the results of the sensitivity study. The marginal posterior probabil-
ity for locus i , l i and P ( l i |
|
M i |
=36 , max
|
M i |
=55 , max
|
M i |
=78 and max
|
M i |
D ) is given for the five loci with the highest probability.
Notice that regardless of the restriction setting, locus ATHCHIB 2 is deemed most
probable. This agrees with previous studies using this data set. In addition, the second
and third most probable loci agree across restriction settings. However, these loci have
low probability. One other trait to notice is that no epistatic terms appear in the highest
marginal loci. The fact that no epistatic effects appear significant is not a result of the
restriction set.
Ta b l e 2 . Activation probabilities of locus i , l i for restriction parameter r =8 , 10 , 12 and 14
r =8
r =10
max|M i | =36
max|M i | =55
l i
P ( l i |D )
l i
P ( l i |D )
ATHCHIB2
0.699
ATHCHIB2
0.751
MSAT5-9
0.415
MSAT5-9
0.481
MSAT5-22
0.402
MSAT5-22
0.445
MSAT5-12
0.291
MSAT5-12
0.331
MSAT1-5
0.271
MSAT2-36
0.327
r =12
r =14
max|M i | =78
max|M i | = 105
l i
P ( l i |D )
l i
P ( l i |D )
ATHCHIB2
0.735
ATHCHIB2
0.733
MSAT5-9
0.509
MSAT5-9
0.516
MSAT5-22
0.473
MSAT5-22
0.511
MSAT2-36
0.380
MSAT2-36
0.441
MSAT1-5
0.373
MSAT1-5
0.434
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