On the Analysis of Optical Mapping Data - University of Wisconsin ...

45
Mean spurious score
0
−10
−20
Number of fragments
20 40 60
Length (Kb)
400 600 800 1000
Regression Fit
−30 −20 −10 0
Counts
6630
5837
5094
4402
3760
3169
2628
2138
1698
1309
971
683
445
259
122
36
1
Figure 3.5 Parametric models for µ(M). The average of four spurious scores for each map is
plotted against the number of fragments N, the length L, and the fitted values from a linear
model with terms N, L and their product NL. The multiple regression model explains more
of the variability, and also suggests better symmetry.
3.5 demonstrates the utility of this approach. As before, a generalized least squares model
with standard deviation linear in the fitted values is more appropriate, giving standardized
test statistics
)
S
(˜G|M − ˜µ (M)
T 2 (M) =
̂δ 2 − ˜µ (M)
where ˜µ (M) are the fitted responses.
Comparison: Table 3.1 summarizes the results from both approaches. Specifically, the
mean spurious scores for each of the 206796 GM07535 maps were estimated using n = 4
permutations of the reference. A fifth permutation was used for parameter estimation: δ 1
in the direct approach, δ 2 and the regression coefficients in the regression approach. A sixth
permutation was used to sample from the null distributions, and 99% and 99.9% cutoffs
were determined by the appropriate quantiles of these samples of size 206796. The two
approaches largely agree in both cases. For aligning a future map, the regression method
is of more practical value, as it would require only one alignment to ˜G, whereas the direct
method would require additional alignments to several permuted references to estimate µ(M).