A Definition of Conditional Probability with Non-Stochastic Information

Area of Science:

• Probability theory
• Decision theory
• Information theory

Background:

• Traditional conditional probability relies solely on stochastic (random) information for updates.
• Limitations exist in applying probability updates to deterministic or non-random information sources.

Purpose of the Study:

• To define conditional probability incorporating non-stochastic information.
• To extend the framework of probability updating beyond random events.
• To provide a rigorous, axiomatically derived definition.

Main Methods:

• Development of a new axiomatic framework for conditional probability.
• Integration of a loss function to link non-stochastic information to outcomes.
• Formal derivation of the conditional probability definition.

Main Results:

• A novel definition of conditional probability that accepts non-stochastic information.
• The proposed definition is grounded in a set of axioms.
• Demonstration through an illustrative example.

Conclusions:

• The new definition broadens the applicability of conditional probability.
• Enables probability updates with deterministic information, enhancing decision-making.
• Offers a foundation for further research in non-stochastic information processing.