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p + γ t
2
q ( M t |
M c )
q ( M c |
p + γ c
2
.
M t ) =
(15)
3
Simulation Study
×
To validate this approach, loci information from Arabidopsis thaliana Bay-0
Shah-
dara was used. Figure 2 illustrates the genetic map of the Arabidopsis thaliana Bay-0
×
Shahdara,which has five chromosomes and a total of 38 markers. For this simulation
study, 158 lines were used.
I
II
III
IV
V
0
T 1G11
F21M 12
M SA T 2-5
M SA T 2-38
NGA172
ATHCHIB2
M SA T 4-39
M SA T 4-8
M SA T 11-0
NGA8
M SA T 4-35
M SA T 4-15
25
M SA T 3-19
M S A T 5-14
NGA139
M SA T -36
M SA T 2-41
M SA T 2-7
NG A 248
M SA T 3-32
M SA T 3-21
M S A T 5-22
T 27K 12
50
M SA T 4-18
M SA T 4-9
M SA T 2-10
M SA T 2-22
M S A T 5-9
NG A 128
F5I14
M SA T 1-13
M SA T 3-18
M S A T 5-12
75
M SA T 4-37
M S A T 5-19
M SA T 1-5
G eneti c M ap
BAY-0 x SHADARA
100
cM
Fig. 2. Genetic map of the Arabidopsis Thaliana Bay-0 by Shahdara
Using the loci matrix from the Arabidopsis thaliana dataset two loci X A and X B
were randomly selected from the possible loci and the following model was used to
generate the data:
y i = δX Ai + δX Bi + δX Ai X Bi + i ,
(16)
where δ is the effect size, i
N (0 , 1) . Each dataset contained a sample size of 158
observations. Effect sizes of 0 , 1 / 2 , 1 , 3 / 2 , 2 , 5 / 2 , 3 , 7 / 2 , 4 , 9 / 2 and 5 were generated.
Each of these effect sizes was repeated 10 times.
Using the data set and the method proposed the following probabilties were cal-
culated: P ( X A |
X A ,X B ,D ) .Thesewere
calculated for 110 simulated data sets. Using the following prior distributions β j
N (0 , 200) and σ 2
D ) , P ( X B |
D ) , P ( X AB |
D ) and P ( X AB |
χ 2 (1) for the model parameters and P ( M i ) is uniform over the
all models subject to the restriction of r =10 . For each simulated data set 5 chains of
16,000 samples were taken from the posterior distribution of the models, with the first
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