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Bayes’ theorem

• Intuition disregards the base rate;
• Bayes taught us to regard it.
• If you think about whether a mammogram
• detects breast cancer,
• you must consider the base rate—
• the prevalence of breast cancer.
• If a mammogram shows
• you have breast cancer
• and the diagnosis is accurate
• only 80 percent of the time
• but only one person in a hundred
• gets breast cancer,
• then your chance of having it is
• only about 7.8 percent.

Bayes’ interpreters

• Thomas Bayes was lucky in that after he died,
• Richard Price became his literary executor,
• edited his work, wrote an introduction,
• and presented it to the Royal Society.
• Pierre-Simon Laplace developed
• the Bayesian interpretation of probability,
• unaware of the work of Bayes and Price,
• so I might have been writing about Laplace’s theorem.

Training

• Something funny about the human brain,
• might be a throwback to an evolutionary stage
• or a limitation of the structure of its synapses,
• but it needs training from early childhood,
• socializing experiences, help from loved ones,
• continuing stimulation, and constant reminders.