Hierarchical Bayes Small Area Estimation for Rice Yield Using Remote Sensing Data

There is a growing interest in model based Small Area Estimation (SAE) techniques for providing reliable estimates for small areas. In this research, we apply Hierarchical Bayes (HB) SAE technique that borrow strength across blocks using remotely-sensed auxiliary variable to predict yield of rice crop in Kurukshetra district of Haryana. The HB method effectively handles complex small area models using Markov Chain Monte Carlo (MCMC) technique to manage high-dimensional posterior integrations. The potential scale reduction factor <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"> <mml:mrow> <mml:mover> <mml:mi>R</mml:mi> <mml:mo stretchy="false">^</mml:mo> </mml:mover> </mml:mrow> </mml:math> was used to determine the success of convergence of the HB model. The efficiency of HB estimators is compared with the Fay Herriot (FH) and direct estimator. The study indicates that by borrowing strength from similar areas and incorporating a weakly informative prior for model parameters, HB estimators significantly reduce variance compared to traditional empirical based linear unbiased prediction (EBLUP) and direct estimator. Performance validation of the models is conducted using statistical metrics such as Coefficient of Variation (CV) and Bias plots. Assessments of potential bias introduced by HB estimators, in contrast to the direct and FH estimator, show minimal to negligible additional bias. This research underscores the advantages of employing SAE within a Hierarchical Bayesian framework, enabling more accurate inference at the block level and offering valuable insights for agricultural planning and decision-making.