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2023•Revista de la Real Academia de Ciencias Exactas Físicas y Naturales Serie A MatemáticasOpen access

Conditional probability and probability updating

José Manuel Gutiérrez Díez

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Abstract

Abstract The conditional probability formula is supposed to reflect the correct updating of probability assignments when new information is incorporated. Starting from a non-atomic probability measure, it is proved that the conditional probability formula provides the only transformed probability measure satisfying a “minimum requirement” relational assumption. This result applies to the standard Bayesian parametric model.

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Abstract The conditional probability formula is supposed to reflect the correct updating of probability assignments when new information is incorporated. Starting from a non-atomic probability measure, it is proved that the conditional probability formula provides the only transformed probability measure satisfying a “minimum requirement” relational assumption. This result applies to the standard Bayesian parametric model.

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Available abstract

Abstract The conditional probability formula is supposed to reflect the correct updating of probability assignments when new information is incorporated. Starting from a non-atomic probability measure, it is proved that the conditional probability formula provides the only transformed probability measure satisfying a “minimum requirement” relational assumption. This result applies to the standard Bayesian parametric model.

Key concepts: Regular conditional probability, Conditional probability, Probability measure, Law of total probability, Chain rule (probability), Measure (data warehouse), Empirical probability, Mathematics

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