The ratio of marginal likelihoods of two competing models, BF12 = p(data | M1) / p(data | M2). Quantifies the evidence the data provide for one model over another, updating prior model odds to posterior model odds. Kass & Raftery (1995) propose conventional thresholds (BF > 3 substantial, > 10 strong, > 100 decisive). Sensitive to prior specification; used cautiously in modern workflow.