What is Bayesian updating?

Definition

Bayesian updating starts with a prior distribution that represents uncertainty before observing new data. Bayes' rule combines that prior with the likelihood of the observed evidence to produce a posterior distribution, which becomes the updated account of what is plausible.

The method supports continuous learning from evidence without pretending that one observation creates certainty. Results still depend on the prior, the likelihood model, and data quality. In practice, teams should examine sensitivity to those choices and test whether repeated probability estimates are calibrated.

ELI5

Bayesian updating is a way to revise a probability when new evidence arrives. It combines what was believed before with how likely the new evidence would be under each possible explanation.

For example, a system may initially think a machine failure is unlikely, then raise that probability after seeing an unusual sensor reading. The update does not create certainty, and the result still depends on the starting belief, the sensor's reliability and the quality of the model used to interpret it.

Acronyms and aliases

Bayesian update variant

Frequently asked questions

What are the main parts of Bayesian updating?

The main parts are a prior distribution, an evidence likelihood, and the posterior distribution produced after combining them with Bayes' rule.

Does Bayesian updating remove uncertainty?

No. It revises uncertainty in light of evidence, and the result can remain broad when the evidence is weak, noisy, or incomplete.

Videos explaining Bayesian updating