  We present an approach to estimate an upper bound for the impact probability
of a potentially hazardous asteroid when part of the force model depends on
unknown parameters whose statistical distribution needs to be assumed. As case
study we consider Apophis' risk assessment for the 2036 and 2068 keyholes based
on information available as of 2013. Within the framework of epistemic
uncertainties, under the independence and non-correlation assumption, we assign
parametric families of distributions to the physical properties of Apophis that
define the Yarkovsky perturbation and in turn the future orbital evolution of
the asteroid. We find ${\rm IP}\leq 5\times 10^{-5}$ for the 2036 keyhole and
${\rm IP}\leq 1.6\times 10^{-5}$ for the 2068 keyhole. These upper bounds are
largely conservative choices due to the rather wide range of statistical
distributions that we explored.

Earth and Planetary Astrophysics;Optimization and Control