Posterior probability represents an updated belief after observations modify an initial prior. In click modeling, it estimates a document’s relevance after incorporating clicks and examinations. section 11.3.2
A beta prior encodes an initial relevance grade and its strength. Each click increases posterior_a; each examination without a click increases posterior_b. The posterior mean, posterior_a divided by their sum, becomes the beta-adjusted relevance grade. section 11.3.2
Tune the prior deliberately:
- Use a stronger prior to make individual clicks move estimates less, or a weaker prior to make them move more. section 11.3.2
Blue-ray query
With prior_grade 0.3 and prior_weight 100, a document recording 14 clicks and 34 examinations produces posterior_a 44, posterior_b 90, and beta_grade 0.328358. The prior pulls sparse or extreme estimates toward 0.3.
