Bayesian inference for agronomic response models: Application to critical soil test value estimation

Values from agronomic response models underpin fertilizer recommendations but are often treated as fixed estimates from a single model. Using soil test phosphorus (P), we compared likelihood‐based and Bayesian approaches for estimating critical soil test values (CSTVs) and further evaluated probabilistic inference and Bayesian model averaging (BMA). Quadratic‐plateau (QP) and Bayesian quadratic‐plateau (B‐QP) models were fitted to datasets comprising 30 and 15 site‐years, respectively. For 30 and 15 site‐year datasets, point estimates were similar (16 vs. 15 mg kg −1 and 19 vs. 17 mg kg −1 , respectively). Probability surfaces quantified the likelihood of response, reframing inference as response risk rather than a single breakpoint. Bayesian model averaging across plateau and exponential forms yielded a model‐averaged CSTV of 14 mg kg −1 (95% credible interval: 8–33), accounting for both structural and parameter uncertainty. This approach can be applied to other nutrients in agronomic studies.