A Restricted Model Space Approach for the Detection of Epistasis in Quantitative Trait Loci Using Markov Chain Monte Carlo Model Composition - Agents and Artificial Intelligence - page 106

0 0.5 1 2 4 0 0.5 1 2 4

Effect Size Effect Size

Fig. 4. Boxplots of epistatic effect activation probabilities (left) and conditional activation proba-
bilities for epistatic effects (right) for effect sizes 0, 1 / 2, 1, 2 and 4 using 100 simulated data sets
per effect size. Dashed line at 1 / 2 is for reference.

4 Example

The Arabidopsis thaliana is a model plant for genetic experiments in that it is easily
genetically manipulated. The response of interest is the angle of the cotyledon opening
that ranges from 0 degrees (no opening) to 180 degrees (fully opened). The cotyledon
is the is the first embryonic leaves on a seedling plant. The wider the opening angle the
more viable the mature plant.For each of the 158 lines at each of the 38 loci (markers) a
value of 1 or -1 corresponding to whether the marker at that location came from parent
A or parent B, respectively (unknown loci information is coded with a 0). With this data
and using an unrestricted model space the largest model would have 741 terms. Hence,
many models can not be fit. By restricting the model space to r =10 the largest model
would have 55 terms and thus, all models have enough observations to be estimated.
To determine if any aliasing between the main effects and interaction terms occured
the data was screened. This screening showed that no interaction terms are aliased with
any main effect term. Hence, conclusions about the main effect terms will not be con-
founded with any epistatic effects. An additional screen of the data was performed to
determine if there is aliasing between any interaction effects. Aliased interaction effects
were noted for consideration during posterior inferences.
For this example, the exact marginal posterior probability of the data given model M c
was computed using equation (6) and the proposed MC 3 method with restricted model
space was utilized. For each model under consideration the prior distributions for the
model parameters were defined as: β j ∼ N (0 , 200) for all j and β jk ∼ N (0 , 200) for