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

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resulting in an unusually large sizing error for that particular fragment. The image processing
step attempts to control such errors, but they can not be eliminated entirely.
2.2 Parameter estimation
Estimation of parameters in the stochastic model described above is difficult, but it is
important for several reasons. First, estimates of the parameters are required in certain
fundamental procedures. For example, likelihood ratio based score functions are expressed
in terms of model parameters, and exact values of the parameters are required to completely
define the score. Parameter values are also required for null distributions used in determining
p-values for potential genomic variations (Reslewic et al.). Second, estimates are necessary
in order to simulate optical maps. Due to the complex nature of the data, simulation is
often the only reasonable approach to investigate the operating characteristics of various
inferential procedures, despite the fact that the model may not capture all the variability in
real data. Simulation can also be a useful tool in directing laboratory research, since it can
provide guidance about which aspects of the experiment have the maximum impact on the
final results.
Difficulty: The difficulty in estimation arises primarily because the true restriction map
is rarely known. Even for optical maps from genomes whose sequence (and hence restriction
map) is completely known, the correspondence between cut sites in observed optical maps
and recognition sites in the true restriction map are never known with certainty. In fact,
inferring this correspondence is precisely the goal of alignment. One possibility is to assume
the correctness of alignments that are declared to be statistically significant, and then use
these alignments for estimation. We will briefly discuss such methods, noting that the
resulting estimates are likely to be biased. A secondary difficulty in estimation is due to the
fact that the parameters may not remain constant over the course of an experiment. This is
difficult to address, and we can only assume that the changes are not substantial enough to