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

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µ
(52.1,448]
(37.3,52.1]
(29.9,37.3]
(24.9,29.9]
(21.2,24.9]
(18.2,21.2]
(15.6,18.2]
(13.6,15.6]
(11.7,13.6]
(10,11.7]
(X − µ) µ
(X − µ) µ
(X − µ) τ 2 µ 2 + σ 2 µ(τ 2 + 1)
−4 −2 0 2
−0.6 −0.4 −0.2 0.0 0.2 0.4
−6 −4 −2 0 2 4 6
Figure 2.4 Variance models for observed fragments sizes. The dependence of the variance
on the true fragment length µ is difficult to study because the true fragment lengths are unknown.
However, given a reasonable alignment scheme, the true lengths are known if highly
significant alignments are assumed to be true. Here, we use significant alignments of the
GM07535 data, leaving out all fragments less than 10 Kb since smaller fragments may have
a different variance model. To remove possible effects of within-map dependence, only one
fragment is randomly selected from each map. The plots are box and whisker plots of lengths
standardized according to different variance models, compared across different ranges of µ.
Clearly, the first two variance models do not completely capture the systematic dependence
on µ, but the last one does. The large proportion of ‘outliers’ suggests non-normality, which
is explored further in Figure 2.5.
−4 −2 0 2 4
Normal
t with 5 d.f.
X − µ
τ 2 µ 2 + σ 2 µ(τ 2 + 1)
2
0
−2
−4 −2 0 2 4
Theoretical Quantiles
Figure 2.5 Distribution of standardized fragment length errors. The data used in Figure
2.4 are used again in Q-Q plots to illustrate that the observed lengths are non-normal.
Empirically, the t distribution seems to be a better fit.