Bayes’ rule prescribes updating beliefs in proportion to incoming evidence

Evidence

When the English economist, John Maynard Keynes, was once challenged for changing his position on an issue, he reportedly replied: ‘When the facts change, I change my mind. What do you do, sir?’ Scientists argue a lot over models that convincingly explain how the human brain reasons about evidence. If the brain were optimally attuned to processing evidence, many of us think the brain would be ‘Bayesian’. Bayes’s theorem was named after the eighteenth-century English mathematician Reverend Thomas Bayes and his work on conditional probabilities. In its simplest form, Bayes’s rule can be thought of as a formula for how to update probabilities that certain hypotheses we might have about the world are true, given the available evidence. In other words, you might have established some prior beliefs about an event (for example, that NASA faked the moon landing). You then encounter a piece of evidence – such as a statistic or fact – which strongly contradicts this belief (such as the 300 kilos of verified moon rock that the astronauts brought back). Following a Bayesian approach, you would update your new (formally called ‘posterior’) belief in accordance with this evidence. — Sander van der Linden, Foolproof, 102

Categorization

• DEFINE: Clears, concrete definition of Bayesian updating via prior/posterior with a live worked example.
• XREF: connects to: Bayes’ rule is the unique rational way to update belief — Cailin O’Connor and James Owen Weatherall, The Misinformation Age: How False…, 108; Belief systems respond to contrary evidence by discounting the evidence; Trustworthiness beliefs are updated through a Bayesian-style learning process. (+6 more)

Broader Connections

• Bayes’ rule is the unique rational way to update belief #expands (1.00) — Cailin O’Connor and James Owen Weatherall, The Misinformation Age, 108
• Trustworthiness beliefs are updated through a Bayesian-style learning process. #exemplifies (0.90)
• Belief systems respond to contrary evidence by discounting the evidence #contradicts (0.85)
• Disconfirming evidence can strengthen rather than weaken committed beliefs. #complicates (0.85) — Philip Mirowski, Never Let a Serious Crisis Go to Waste, 97
• People often resist or reverse belief updating rather than tracking evidence #contradicts (0.80) — Sander van der Linden, Foolproof, 104
• Initial stereotypes bias perception of identical evidence to confirm themselves #contradicts (0.80) — John F. Dovidio, Peter Glick, Laurie A. Rudman, On the Nature of Prejudice, 1175
• Even the most partisan reasoners eventually change beliefs under repeated corrective evidence #qualifies (0.80) — Lee McIntyre, Post-Truth, 110
• Confirmation bias and inertia make reputations resistant to disconfirming evidence #contradicts (0.80)
• More confirming instances increase the probability of an inductive conclusion. #qualifies (0.75) — Ruggero J. Aldisert, Agatha D. Aldisert, Logic for Lawyers- A Guide to Clear…, 567