What Bayesian Updating Is
Bayesian updating is the practice of revising confidence by combining prior expectations with new evidence.
The Intuition
Bayesian updating begins with a modest idea: new evidence should change confidence differently depending on what was already plausible. If a common cause and a rare cause both explain a symptom, the common cause usually deserves more initial weight. If a new observation is much more expected under one hypothesis than another, confidence should move toward the hypothesis that predicted it better.
In everyday language: start with a reasonable prior, ask how expected the evidence is under each live possibility, then update proportionally.
Priors Are Not Prejudices
A prior is a starting estimate before the newest evidence is considered. Priors can be abused, especially when they are just stereotypes wearing mathematical clothing. But the idea of a prior is unavoidable. Every inquiry begins somewhere: with base rates, background knowledge, past reliability, physical possibility, or the track record of similar claims.
The question is not whether we have priors. The question is whether our priors are explicit, relevant, revisable, and scaled appropriately.
Likelihoods Do the Moving
The likelihood asks how expected the evidence would be if a hypothesis were true. If a test result is common among people with a disease and rare among people without it, the result moves confidence toward the disease hypothesis. If the result is common in both groups, it should move confidence only a little.
This is why vivid evidence is not automatically strong evidence. Strong evidence discriminates. It helps separate live possibilities.
Updating and the Credencing Model
Bayesian updating mostly lives in the movement from objective evidence to perceived evidence. It is a deep-rational tool: a way to process support more accurately. But the Credencing model adds a second question. After the update is perceived, does the agent actually assign the credence the update warrants?
A person can understand the math and still refuse the conclusion. That is why the model distinguishes deep rationality from core rationality.
Adjacent References
These are starting points rather than exhaustive citations. They connect this page to nearby work in probability, calibration, cognitive bias, and social epistemology.
- |Thomas Bayes, "An Essay towards solving a Problem in the Doctrine of Chances" (1763).
- |E. T. Jaynes, Probability Theory: The Logic of Science (2003).