A Definition of Conditional Probability with Non-Stochastic Information

Pier Giovanni Bissiri; Stephen G Walker

doi:10.3390/e20080572

A Definition of Conditional Probability with Non-Stochastic Information

Entropy (Basel). 2018 Aug 3;20(8):572. doi: 10.3390/e20080572.

Authors

Pier Giovanni Bissiri¹, Stephen G Walker²

Affiliations

¹ School of Mathematics, Statistics and Physics, Herschel Building, Newcastle University, Newcastle upon Tyne NE1 7RU, UK.
² Department of Mathematics, University of Texas at Austin, 2515 Speedway, Austin, TX 78712, USA.

Abstract

The current definition of a conditional probability enables one to update probabilities only on the basis of stochastic information. This paper provides a definition for conditional probability with non-stochastic information. The definition is derived by a set of axioms, where the information is connected to the outcome of interest via a loss function. An illustration is presented.

Keywords: conditional probability; loss function; non-stochastic information.