The aim of this paper is to show that the concept of probability is best understood by dividing this concept into two different types of probability, namely physical probability and analogical probability. Loosely speaking, a physical probability is a probability that applies to the outcomes of an experiment that have been judged as being equally likely on the basis of physical symmetry. Physical probabilities are arguably in some sense 'objective' and possess all the standard properties of the concept of probability. On the other hand, an analogical probability is defined by making an analogy between the uncertainty surrounding an event of interest and the uncertainty surrounding an event that has a physical probability. Analogical probabilities are undeniably subjective probabilities and are not obliged to have all the standard mathematical properties possessed by physical probabilities, e.g. they may not have the property of additivity or obey the standard definition of conditional probability. Nevertheless, analogical probabilities have extra properties, which are not possessed by physical probabilities, that assist in their direct elicitation, general derivation, comparison and justification. More specifically, these properties facilitate the application of analogical probability to real-world problems that can not be adequately resolved by using only physical probability, e.g. probabilistic inference about hypotheses on the basis of observed data. Careful definitions are given of the concepts that are introduced and, where appropriate, examples of the application of these concepts are presented for additional clarity.
翻译:本文的目的是表明,对概率概念的最佳理解是将这个概念分为两种不同的概率,即物理概率和类比概率。粗略地说,物理概率是一种适用于实验结果的概率,而实验结果根据物理对称判断具有同等可能性。物理概率在某种意义上可以说是“客观”的,并具有概率概念的所有标准特性。另一方面,模拟概率的定义是通过类比围绕感兴趣事件的不确定性与具有物理概率的事件的不确定性之间的比值来界定的。无可否认的是,物理概率是一种主观概率,没有义务拥有物理概率所具备的所有标准数学特性,例如,它们可能不具备相加性属性或符合有条件概率标准定义的属性。然而,模拟概率具有额外的特性,这些特性并非由物理概率所具备的,有助于直接推断、一般推断、比较和解释。更具体地说,这些特性有助于将类比概率应用于物理概率,而在实际概率概念中,无法充分看到这些精确的概率定义,因此,在实际概率的精确性概念中,不能通过精确性定义加以理解。