The diachronic Bayesian

08/24/2023

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by   Vladimir Vovk, et al.

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It is well known that a Bayesian's probability forecast for the future observations should form a probability measure in order to satisfy natural conditions of coherency. The topic of this paper is the evolution of the Bayesian's probability measure in time. We model the process of updating the Bayesian's beliefs in terms of prediction markets. The resulting picture is adapted to forecasting several steps ahead and making almost optimal decisions.