bayes-factor-ratio-marginal-likelihoods
IN premise — summaries/2026/08/24/wiki-Bayesian_inference-chunk-3.md
Created 2026-08-25T02:58:43+00:00
The Bayes factor is the ratio of marginal likelihoods (evidence) of two competing models and is distinct from a simple likelihood ratio because it integrates over the full parameter space.
Summary
When comparing two competing explanations, the Bayes factor averages each one's predictive power across all possible parameter settings rather than just checking how well each fits at its best guess. This matters because it naturally penalizes overly complex models: spreading probability across a wider range of possibilities dilutes the average predictive strength, so a simpler model that concentrates its predictions wins out unless the extra complexity is genuinely needed.