Four interpretations of single-case conditional propensities are described and it is shown that for each a version of what has been called ‘Humphreys’ Paradox’ remains, despite the clarifying work of Gillies, McCurdy and Miller. This entails that propensities cannot be a satisfactory interpretation of standard probability theory.

Conditional distribution reflects the dependency link among random variables, but two-dimensional random variables Conditional Distribution has some limitations. In order to rich the content of conditional distribution this paper gives the extension of conditional distribution and examples in the case of continuous random variables. For the given definition of conditional distribution of three-...

We provide a simple example showing that some conditional information inequalities (even in a weak form) cannot be derived from unconditional inequalities.

We apply Pires’s coherence property between unconditional and conditional preferences that admit a CEU representation. In conjunction with consequentialism (only those outcomes on states which are still possible can matter for conditional preference) this implies that the conditional preference may be obtained from the unconditional preference by taking the Full Bayesian Update of the capacity....

A sender communicates with a receiver who wishes to reliably evaluate a function of their combined data. We show that if only the sender can transmit, the number of bits required is a conditional entropy of a naturally deened graph. We also determine the number of bits needed when the communicators exchange two messages.

We deal with information measures and we introduce a suitable notion of conditional independence by studying the main properties.

In several economic applications (e.g. marketing research, microsimulation models) there is the need to consider different data sources and to integrate the information coming from them. In this paper we show how integration problems can be managed by means of coherence for partial conditional probabilistic assessments. Coherence allows us to combine the knowledge coming from the different sour...

We present a logical notion of conditional independence, discuss its key properties, and review several of its formulations and applications.