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Reasoning under uncertainty
  1. Colin Aitken1,
  2. Dimitris Mavridis2,3
  1. 1School of Mathematics, Maxwell Institute and Joseph Bell Centre for Forensic Statistics and Legal Reasoning, University of Edinburgh, Edinburgh, UK
  2. 2Department of Primary Education, University of Ioannina, Panepistimioupoli, Ioannina, Greece
  3. 3School of Medicine, Paris Descartes University, Paris, France
  1. Correspondence to Professor Colin Aitken; C.Aitken{at}ed.ac.uk

Abstract

Introduction It is difficult to reason correctly when the information available is uncertain. Reasoning under uncertainty is also known as probabilistic reasoning.

Methods We discuss probabilistic reasoning in the context of a medical diagnosis or prognosis. The information available are symptoms for the diagnosis or diagnosis for the prognosis. We show how probabilities of events are updated in the light of new evidence (conditional probabilities/Bayes’ theorem). A resolution is explained in which the support of the information for the diagnosis or prognosis is measured by the comparison of two probabilities, a statistic also known as the likelihood ratio.

Results The likelihood ratio is a continuous measure of support that is not subject to the discrete nature of statistical significance where a result is either classified as ‘significant’ or ‘not significant’. It updates prior beliefs about diagnoses or prognoses in a coherent manner and enables proper consideration of successive pieces of information.

Discussion Probabilistic reasoning is not innate and relies on good education. Common mistakes include the ‘prosecutor’s fallacy’ and the interpretation of relative measures without consideration of the actual risks of the outcome, for example, interpretation of a likelihood ratio without taking into account the prior odds.

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Footnotes

  • Patient consent for publication Not required.

  • Contributors CA and DM contributed to writing and commenting on this paper.

  • Funding The authors have not declared a specific grant for this research from any funding agency in the public, commercial or not-for-profit sectors.

  • Competing interests None declared.

  • Provenance and peer review Not commissioned; externally peer reviewed.

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