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

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states will usually lead to over-fitting: some estimated states may be close to each other and
rare states may not be identified at all. In practice, diagnostic plots and numerical criteria
like AIC and BIC may assist in making the choice. The estimated negative binomial size
parameter may also serve as a guide, since too few states in the model will be compensated
for by stronger apparent extra-Poisson variation. External information, when available, may
be used to put further constraints on the parameters, e.g. fixing the mean states up to a
multiplicative constant, which is estimated.
Normal state: The HMM does not assign the special label of“normality”to any particular
state. However, the initial choice of intervals are determined to have a specified mean number
of hits under the hypothesis of no copy number changes. In practice, the mean of the
stationary distribution of the estimated HMM is usually close to this initial choice. The
estimated mean state with the highest (stationary) probability is usually also the one closest
to this initial choice, and can be considered to be the normal state. This should work well
unless there is widespread CNP, in which case the definition of “normal state” is unclear.
Alignment: Alignment of optical maps to the in silico reference is an important prerequisite
for our analysis. Although we expect and correct for non-uniform sensitivity, the
alignment scheme should nonetheless be as sensitive as possible with a low false positive rate.
In our examples, we have used the SOMA score function (A.1) with default parameters. The
determination of significance thresholds is discussed in Chapter 3. All alignments used were
significant at a nominal specificity of 99.9%.
Symmetry: High and low coverage are not treated symmetrically, in the sense that the
power to detect lowered coverage may be lower than that to detect elevated coverage of the
same relative magnitude. Thus, it may make sense to reverse the roles of the normal data
and the dataset of interest, so that low coverage is identified as high mean states in the
HMM. Of course, the relative sizes of the data sets are also relevant.