  The detection of change-points in heterogeneous sequences is a statistical
challenge with applications across a wide variety of fields. In bioinformatics,
a vast amount of methodology exists to identify an ideal set of change-points
for detecting Copy Number Variation (CNV). While considerable efficient
algorithms are currently available for finding the best segmentation of the
data in CNV, relatively few approaches consider the important problem of
assessing the uncertainty of the change-point location. Asymptotic and
stochastic approaches exist but often require additional model assumptions to
speed up the computations, while exact methods have quadratic complexity which
usually are intractable for large datasets of tens of thousands points or more.
In this paper, we suggest an exact method for obtaining the posterior
distribution of change-points with linear complexity, based on a constrained
hidden Markov model. The methods are implemented in the R package postCP, which
uses the results of a given change-point detection algorithm to estimate the
probability that each observation is a change-point. We present the results of
the package on a publicly available CNV data set (n=120). Due to its
frequentist framework, postCP obtains less conservative confidence intervals
than previously published Bayesian methods, but with linear complexity instead
of quadratic. Simulations showed that postCP provided comparable loss to a
Bayesian MCMC method when estimating posterior means, specifically when
assessing larger-scale changes, while being more computationally efficient. On
another high-resolution CNV data set (n=14,241), the implementation processed
information in less than one second on a mid-range laptop computer.
