Concept

Odds form — where it appears

Writing Bayes' rule as prior odds times a likelihood ratio, which turns updating into multiplication. It makes the effect of a second test on the same condition immediate, since the likelihood ratios simply multiply where the probabilities do not.

Named by 2 essays across 2 fields — each of them below, with the objects they name alongside it.

What a positive test means, sensitivity 90%, specificity 95%. At a prevalence of one in a thousand, 98 of every hundred positives are false. At one in 10, 33 are. The test has not changed.

What a positive test is worth

A test that is 90% sensitive and 95% specific sounds accurate. For a condition affecting one person in a thousand, 98% of its positive results are wrong, and a worse test on a commoner condition beats a better test on a rare one.

paradox · Baserate

The base rate was always Bayes

The screening arithmetic everybody finds counter-intuitive is a posterior update with a prior of one in a thousand. Naming it that way turns a famous puzzle into an instance of a rule, and makes the sequential version obvious.

bayes · Baserate

Named alongside it

The objects these essays reach for when they reach for this one.

Base rate Predictive value Prior Screening Base rate fallacy The Bayes factor False positive p-value Positive predictive value Posterior Sensitivity and specificity Sequential testing

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