This research introduces a new constraint domain for reasoning about data
with uncertainty. It extends convex modeling with the notion of p-box to gain
additional quantifiable information on the data whereabouts. Unlike existing
approaches, the p-box envelops an unknown probability instead of approximating
its representation. The p-box bounds are uniform cumulative distribution
functions (cdf) in order to employ linear computations in the probabilistic
domain. The reasoning by means of p-box cdf-intervals is an interval
computation which is exerted on the real domain then it is projected onto the
cdf domain. This operation conveys additional knowledge represented by the
obtained probabilistic bounds. Empirical evaluation shows that, with minimal
overhead, the output solution set realizes a full enclosure of the data along
with tighter bounds on its probabilistic distributions.

该研究引入了一种新的约束域，用于推理关于带有不确定性的数据。它通过引入概率区间的概念，将凸建模扩展到新的领域，以获得关于数据位置的额外可量化信息。通过实验证明，使用 p-box cdf 间隔进行推理可以实现数据的完全包含以及更紧的概率分布范围限制。