Benchmarking Evaluation of Gaussian-Process Emulation for Computer Agriculture Soil-Moisture Sensor Networks Under Sparse Calibration: An Artificial Intelligence Posterior-Consistency Bound for Irrigation Scheduling Equity

Sparse calibration of soil-moisture sensor networks in computer agriculture produces Gaussian-process emulators whose posterior credible intervals are used to schedule irrigation, yet the consistency of those intervals under repeated sampling has not been characterised. The study characterises the behaviour of the ordinary least squares estimator under the stated process. Across the 600 replications, the estimated bias was 0.0366 for the intercept and -0.00064 for the exposure coefficient; the root mean squared error was 0.91548 for the intercept and 0.01645 for the exposure coefficient; and empirical coverage of the nominal 95% confidence intervals was 1.0 for both parameters. The sampling distribution of the exposure coefficient was approximately normal and the normal Q-Q plot showed no material departure from Gaussianity. A posterior-consistency bound is derived that links the coverage of the emulator's credible intervals to the sampling coverage of the underlying estimator, and the bound is used to argue that irrigation scheduling equity depends on calibration density rather than on the emulator's interpolation accuracy alone. The contribution is a formal consistency criterion and a benchmarking protocol that together make the equity consequences of sparse calibration auditable before deployment.