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 $${\mathrm{IP}}\le 5\times 10^{-5}$$ for the 2036 keyhole and $${\mathrm{IP}}\le 1.6\times 10^{-5}$$ for the 2068 keyhole. These upper bounds are largely conservative choices due to the rather wide range of statistical distributions that we explored.

中文翻译：

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偶然和认知不确定性下的影响概率

当力模型的一部分取决于需要假设其统计分布的未知参数时，我们提出了一种估计潜在危险小行星撞击概率上限的方法。作为案例研究，我们根据截至 2013 年的可用信息考虑 Apophis 对 2036 和 2068 钥匙孔的风险评估。 在认知不确定性的框架内，在独立和非相关假设下，我们将分布的参数族分配给物理属性Apophis 定义了 Yarkovsky 扰动，进而定义了小行星未来的轨道演化。我们发现 $${\mathrm{IP}}\le 5\times 10^{-5}$$ 为 2036 钥匙孔和 $${\mathrm{IP}}\le 1.6\times 10^{-5}$ $ 2068 钥匙孔。