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

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especially a short noisy one, to originate from somewhere in the reference but have its
optimal alignment somewhere else. The null hypothesis of independence is not true in such
a case, yet we would not want to declare the optimal alignment significant. Thus, it may be
reasonable to define the best spurious score of M against ˜G as the maximum score among
alignments that are not the true alignment. This is of course not observable, since we
have no way of knowing the true alignment, or even whether it exists at all. There are
other problems with this definition; e.g. what makes an alignment sufficiently different from
the true alignment? Should alignments to incorrect but homologous regions be considered
spurious? By formulating the problem as a test of independence, these issues are avoided.
Other methods: Valouev et al. (2006) suggest an approach to determine significance that
is similar to ours in principle, but is completely model-based. They postulate that the
fragment lengths in the reference genome ˜G are i.i.d. exponential variates, and describe a
conditional model for optical maps given the reference. These are then used to formally derive
the marginal distribution of optical maps, which reduces to an i.i.d. exponential distribution
for the optical map fragment lengths, but with a different rate. Cutoffs are obtained by
simulating both reference and optical maps under the null hypothesis of independence. This
is a perfectly valid approach, but may be sensitive to parameter estimates as well as model
misspecification, which is a legitimate concern since their conditional model excludes certain
known sources of noise, namely desorption and scaling (see Chapter 2). Our conditional
non-parametric approach bypasses these concerns.
Direct approach vs regression: Estimating the mean spurious score µ(M) separately
for each map is usually feasible and more powerful than regression. However, for alignments
involving only part of an optical map, a cutoff based on the full map is not appropriate. This
is a concern particularly for overlap matches, where alignments overhanging at the boundary
of the reference map are allowed. The regression approach can still be used in such cases by
considering only the aligned portion of the map. The regression on N and L as used above
is of course not the only possible model, but Table 3.1 suggests that it explains most of the