Quantum Probability Spaces

Quantum Probability Spaces

Categories of Probability Spaces

In this paper, we will show how several important ideas of probability theory can be fit into the framework of category theory by considering two different categories of probability spaces. Once we have defined these categories, we can see several important structures of probability spaces arise in their structure; specifically, we can identify conditional probabilities, subprobability spaces, ...

Crossover in Probability Spaces

This paper proposes a new crossover operator for searching over discrete probability spaces. The design of the operator is considered in the light of recent theoretical insights into genetic search provided by forma analysis. A non-trivial test problem in enforcing coherency of probability estimates in cross-impact analysis highlights the utility of the designed operators. The presented operato...

Geometry on Probability Spaces

Partial differential equations and the Laplacian operator on domains in Euclidean spaces have played a central role in understanding natural phenomena. However this avenue has been limited in many areas where calculus is obstructed as in singular spaces, and function spaces of functions on a space X where X itself is a function space. Examples of the last occur in vision and quantum field theor...

Conditional Probability Spaces

Improper priors are used frequently, but often formally and without reference to a sound theoretical basis. The present paper demonstrates that Kolmogorov’s (1933) formulation of probability theory admits a minimal generalization which includes improper priors and a general Bayes theorem. The resulting theory is closely related to the theory of conditional probability spaces formulated by Renyi...