Intended for healthcare professionals

Education And Debate

Why clinicians are natural bayesians

BMJ 2005; 330 doi: (Published 05 May 2005) Cite this as: BMJ 2005;330:1080

This article has a correction. Please see:

  1. Christopher J Gill, assistant professor (,
  2. Lora Sabin, assistant professor1,
  3. Christopher H Schmid, associate professor2
  1. 1 Center for International Health and Development, Department of International Health, Boston University School of Public Health, Boston, MA 02118, USA,
  2. 2 Biostatistics Research Center, Division of Clinical Care Research, Department of Medicine, Tufts University—New England Medical Center, Boston, MA 02111, USA
  1. Correspondence to: C J Gill
  • Accepted 5 February 2005

Thought you didn't understand bayesian statistics? Read on and find out why doctors are expert in applying the theory, whether they realise it or not


Two main approaches are used to draw statistical inferences: frequentist and bayesian. Both are valid, although they differ methodologically and perhaps philosophically. However, the frequentist approach dominates the medical literature and is increasingly applied in clinical settings. This is ironic given that clinicians apply bayesian reasoning in framing and revising differential diagnoses without necessarily undergoing, or requiring, any formal training in bayesian statistics. To justify this assertion, this article will explain how bayesian reasoning is a natural part of clinical decision making, particularly as it pertains to the clinical history and physical examination, and how bayesian approaches are a powerful and intuitive approach to the differential diagnosis.

A sick child in Ethiopia

On a recent trip to southern Ethiopia, my colleagues and I encountered a severely ill child at a rural health clinic. The child's palms, soles, tongue, and conjunctivae were all white from severe anaemia and his spleen was swollen and firm; he was breathing rapidly, had bilateral pulmonary rales, and was semiconscious. It looked like severe malaria. The clinic's health officer evaluated the child using the integrated management of childhood illness algorithm. The algorithm uses cardinal symptoms such as rapid respiratory rate or fever to classify children as having pneumonia or malaria, or possibly both.

In this case, the child's rapid respiratory rate and absence of fever generated a diagnosis of pneumonia with advice to immediately start antibiotics. Our presence was fortuitous. We were able to give the child antimalarial drugs and transport him to the nearest hospital, where blood smear examination confirmed that his blood was teeming with malaria parasites. How did clinical judgments prove superior to the algorithm, a diagnostic tool carefully developed over two decades …

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