Impact probability under aleatory and epistemic uncertainties

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 IP ≤ 5 × 10 ^{- 5} for the 2036 keyhole and IP ≤ 1.6 × 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.