  Directional detection is a promising search strategy to discover galactic
Dark Matter. Taking advantage on the rotation of the Solar system around the
Galactic center through the Dark Matter halo, it allows to show a direction
dependence of WIMP events. Even though the goal of directional search is to
identify a WIMP positive detection, exclusion limits are still needed for very
low exposure with a rather large background contamination, such as the one
obtained with prototype experiments. Data of directional detectors are composed
of energy and 3D track of recoiling nuclei. However, to set robust exclusion
limits, we focus on the angular part of the event distribution, arguing that
the energy part of the WIMP distribution is featureless and may even be mimic
by the background one. Then, as the angular distributions of both background
and WIMP events are known, a Bayesian approach to set exclusion limits is
possible. In this paper, a statistical method based on an extended likelihood
is proposed, compared to existing ones and is shown to be optimal. Eventually,
a comprehensive study of the effect of detector configuration on exclusion
limits is presented. It includes the effect of having or not sense recognition,
a finite angular resolution, taking into account energy threshold as well as
some astrophysical uncertainties.
