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Countable Additivity and the Foundations of Bayesian Statistics

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Abstract

At a very fundamental level an individual (or a computer) can process only a finite amount of information in a finite time. We can therefore model the possibilities facing such an observer by a tree with only finitely many arcs leaving each node. There is a natural field of events associated with this tree, and we show that any finitely additive probability measure on this field will also be countably additive. Hence when considering the foundations of Bayesian statistics we may as well assume countable additivity over a σ-field of events.

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Authors and Affiliations

  1. Departments of Operational Research and Statistics, London School of Economics, Houghton Street, London, WC2A 2AE, UK

    John V. Howard

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  1. John V. Howard
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Correspondence to John V. Howard.

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Howard, J.V. Countable Additivity and the Foundations of Bayesian Statistics. Theor Decis 60, 127–135 (2006). https://doi.org/10.1007/s11238-005-4594-9

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  • DOI: https://doi.org/10.1007/s11238-005-4594-9

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