Reasoning under uncertainty

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

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.

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.

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.