Fig. 1

Posterior distributions of yield response to plant density model parameters (Eqs. 2 and 3) pooling all 12 combinations of seed treatment, seed size and environment. Derived quantities from these distributions (e.g., the expected value, the standard deviation, and quantiles) were used to build informative priors described in Eqs. 6–10. Purple bars refer to model parameters related to the expected value \({(\mu }_{ij})\) and yellow bars to model parameters related to the variance \({(\sigma }_{ij}^{2})\) of grain yield. Abbreviations: sample size (n), linear term of expected yield response to plant density (\({\beta }_{1}\)), agronomic optimum plant density (AOPD), maximum variance plant density (maxVPD), minimum risk plant density (minRPD), linear term of variance of yield response to plant density (\({\alpha }_{1}\))