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1,000 samples discarded as burn-in samples. The activation probabilities were calcu-
lated using the remaining 75,000 samples.
Figure 3 shows boxplots for the main effect activation probabilities versus the effect
size from the simulated datasets. Notice that for effect sizes of
0
and
1
/
2
the activa-
tion probabilities are low indicating that not much evidence exists for the main effect at
that locus. However, for effect sizes at and above
1
the activation probabilites are quite
high, typically above 0.8. It should be noted that activation probabilities are not associ-
ated with the idea of a p-value and hence cannot be interpreted as such. Furthermore,
the choice of cutoff values for activation probabilities and what is deemed statistically
significant, in the Type I and Type II error sense, has not been studied. However, we
should notice that the activation probabilities for effect sizes at and above
1
are much
larger than those when the effect size is
0
. Hence, one could feel confident that the locus
is important for influencing the observed trait.
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
5
Effect Size
Fig. 3.
Boxplots of main effect activation probabilities for effect sizes 0, 1
/
2, 1, 3
/
2, 2, 5
/
2, 3,
7
/
2, 4, 9
/
2 and 5 using simulated data sets
Figure 4 shows boxplots for activation probabilities of the epistatic effects and the
conditional activation probabilities for epistatic effects versus the effect sizes of
0
,
1
/
2
,
1
,
2
and
4
. Notice that in both plots that both the activation probabilities and the con-
ditional activation probabilities are low for effect sizes
0
and
1
/
2
indicating that the
epistatic effect of the two loci have no minimal effect on the observed trait. However,
notice that for effect sizes larger than
1
the conditional activation probabilities are con-
siderably higher than the standard activation probabilities. Again there has been no
studies of cutoff values for activation probabilities nor conditional activation probabili-
ties. Looking at both the activation probabilities and conditional activation probabilities
with reference to effect size
0
one could feel confident that the two loci work in combi-
nation to influence the observed trait.
