The diachronic Bayesian

Vladimir Vovk

The diachronic Bayesian

Vladimir Vovk

Research output: Contribution to journal › Article › peer-review

Abstract

It is well known that a Bayesian probability forecast for all future observations should be a probability measure in order to satisfy a natural condition of coherence. The main topics of this paper are the evolution of the Bayesian probability measure and ways of testing its adequacy as it evolves over time. The process of testing evolving Bayesian beliefs is modelled in terms of betting. The resulting picture is adapted to forecasting several steps ahead and making almost optimal decisions.

Original language	English
Number of pages	18
Journal	Statistical Science
Publication status	Accepted/In press - 24 Nov 2025

Keywords

Bayesian statistics
probability forecasting
test martingale
decision making

Embargoed Document

Accepted Manuscript
Accepted author manuscript, 466 KB
Licence: CC BY

Cite this

@article{dca1e8bf55b84652bb466194a23431a2,

title = "The diachronic Bayesian",

abstract = "It is well known that a Bayesian probability forecast for all future observations should be a probability measure in order to satisfy a natural condition of coherence. The main topics of this paper are the evolution of the Bayesian probability measure and ways of testing its adequacy as it evolves over time. The process of testing evolving Bayesian beliefs is modelled in terms of betting. The resulting picture is adapted to forecasting several steps ahead and making almost optimal decisions.",

keywords = "Bayesian statistics, probability forecasting, test martingale, decision making",

author = "Vladimir Vovk",

year = "2025",

month = nov,

day = "24",

language = "English",

journal = "Statistical Science",

issn = "0883-4237",

publisher = "Institute of Mathematical Statistics",

}

TY - JOUR

T1 - The diachronic Bayesian

AU - Vovk, Vladimir

PY - 2025/11/24

Y1 - 2025/11/24

N2 - It is well known that a Bayesian probability forecast for all future observations should be a probability measure in order to satisfy a natural condition of coherence. The main topics of this paper are the evolution of the Bayesian probability measure and ways of testing its adequacy as it evolves over time. The process of testing evolving Bayesian beliefs is modelled in terms of betting. The resulting picture is adapted to forecasting several steps ahead and making almost optimal decisions.

AB - It is well known that a Bayesian probability forecast for all future observations should be a probability measure in order to satisfy a natural condition of coherence. The main topics of this paper are the evolution of the Bayesian probability measure and ways of testing its adequacy as it evolves over time. The process of testing evolving Bayesian beliefs is modelled in terms of betting. The resulting picture is adapted to forecasting several steps ahead and making almost optimal decisions.

KW - Bayesian statistics

KW - probability forecasting

KW - test martingale

KW - decision making

M3 - Article

SN - 0883-4237

JO - Statistical Science

JF - Statistical Science

ER -