marginal-likelihood-zero-bayes-failure

IN premisesummaries/2026/08/24/wiki-Bayesian_inference-chunk-2.md

Created 2026-08-25T02:58:43+00:00

If the marginal likelihood p(X|α) equals zero, Bayes' rule cannot be applied because the posterior is undefined.

Summary

When a model assigns zero probability to the data that was actually observed, the Bayesian update breaks down completely because there is no valid posterior to compute. This forces the system to treat the case as a hard failure rather than a routine calculation, since the standard rule for revising beliefs simply cannot produce an answer under those conditions.