  Using observations of cores to infer their intrinsic properties requires the
solution of several poorly constrained inverse problems. Here we address one of
these problems, namely to deduce from the projected aspect ratios of the cores
in Ophiuchus their intrinsic three-dimensional shapes. Four models are
proposed, all based on the standard assumption that cores are randomly
orientated ellipsoids, and on the further assumption that a core's shape is not
correlated with its absolute size. The first and simplest model, M1, has a
single free parameter, and assumes that the relative axes of a core are drawn
randomly from a log-normal distribution with zero mean and standard deviation
\sigma o. The second model, M2a, has two free parameters, and assumes that the
log-normal distribution (with standard deviation \sigma o) has a finite mean,
\mu o, defined so that \mu o<0 means elongated (prolate) cores are favoured,
whereas \mu o>0 means flattened (oblate) cores are favoured. Details of the
third model (M2b, two free parameters) and the fourth model (M4, four free
parameters) are given in the text. Markov chain Monte Carlo sampling and
Bayesian analysis are used to map out the posterior probability density
functions of the model parameters, and the relative merits of the models are
compared using Bayes factors. We show that M1 provides an acceptable fit to the
Ophiuchus data with \sigma o ~ 0.57+/-0.06; and that, although the other models
sometimes provide an improved fit, there is no strong justification for the
introduction of their additional parameters.
