Sparse-Annotation Evaluation for Computer Agriculture Yield Estimators Under Cluster Sampling Frames: An Artificial Intelligence Design-Based Variance Bound for District Planning

Yield estimators built on sparse field annotations are increasingly used to inform district-level agricultural planning, yet their evaluation typically ignores the cluster sampling frame through which the annotations are collected. The bound is derived from a variance-components model in which the between-cluster standard deviation is 6.0, the residual standard deviation is 4.5, and the intraclass correlation is 0.640. A replication-based power analysis across 2000 design cells characterised the operating characteristics of the BACIP estimator for cluster counts of 8, 16, 24 and 32 and effect sizes of 3, 5 and 8 percentage points. The analysis indicates that 54 clusters are required to detect a 5-percentage-point effect at 80% power under the declared variance structure. The bound provides a defensible basis for sizing sparse-annotation evaluations and for interpreting their precision in district planning contexts.