  Some methods aim to correct or test for relationships or to reconstruct the
pedigree, or family tree. We show that these methods cannot resolve ties for
correct relationships due to identifiability of the pedigree likelihood which
is the probability of inheriting the data under the pedigree model. This means
that no likelihood-based method can produce a correct pedigree inference with
high probability. This lack of reliability is critical both for health and
forensics applications.
  In this paper we present the first discussion of multiple typed individuals
in non-isomorphic pedigrees, $\mathcal{P}$ and $\mathcal{Q}$, where the
likelihoods are non-identifiable, $Pr[G~|~\mathcal{P},\theta] =
Pr[G~|~\mathcal{Q},\theta]$, for all input data $G$ and all recombination rate
parameters $\theta$. While there were previously known non-identifiable pairs,
we give an example having data for multiple individuals.
  Additionally, deeper understanding of the general discrete structures driving
these non-identifiability examples has been provided, as well as results to
guide algorithms that wish to examine only identifiable pedigrees. This paper
introduces a general criteria for establishing whether a pair of pedigrees is
non-identifiable and two easy-to-compute criteria guaranteeing identifiability.
Finally, we suggest a method for dealing with non-identifiable likelihoods: use
Bayes rule to obtain the posterior from the likelihood and prior. We propose a
prior guaranteeing that the posterior distinguishes all pairs of pedigrees.
  Shortened version published as: B. Kirkpatrick. Non-identifiable pedigrees
and a Bayesian solution. Int. Symp. on Bioinformatics Res. and Appl. (ISBRA),
7292:139-152 2012.
