Multiple perspectives on the concept of conditional probability

Conditional probability is a key to the subjectivist theory of probability; however, it plays a subsidiary role in the usual conception of probability where its counterpart, namely independence is of basic importance. The paper investigates these concepts from various perspectives in order to shed light on their multi-faceted character. We will include the mathematical, philosophical, and educational perspectives. Furthermore, we will inspect conditional probability from the corners of competing ideas and solving strategies. For the comprehension of conditional probability, a wider approach is urgently needed to overcome the well-known problems in learning the concepts, which seem nearly unaffected by teaching

Metric on a Statistical Space-Time

We introduce a concept of distance for a space-time where the notion of point is replaced by the notion of physical states e.g. probability distributions. We apply ideas of information theory and compute the Fisher information matrix on such a space-time. This matrix is the metric on that manifold. We apply these ideas to a simple model and show that the Lorentzian metric can be obtained if we assumed that the probability distributions describing space-time fluctuations have complex values. Such complex probability distributions appear in non-Hermitian quantum mechanics.Comment: 7 page

A Dutch Book theorem for partial subjective probability

The aim of this paper is to show that partial probability can be justified from the standpoint of subjective probability in much the same way as classical probability does. The seminal works of Ramsey and De Finetti have furnished a method for assessing subjective probabilities: ask about the bets the decision-maker would be willing to place. So we introduce the concept of partial bet and partial Dutch Book and prove for partial probability a result similar to the Ramsey-De Finetti theorem. Finally, we make a comparison between two concepts of bet: we can bet our money on a sentence describing an event, or we can bet our money on the event itself, generally conceived as a set. These two ways of understanding a bet are equivalent in classical probability, but not in partial probability