Cotton yield prediction with Markov Chain Monte Carlo-based simulation model integrated with genetic programing algorithm: a new hybrid copula-driven approach

© 2018 Elsevier B.V. Reliable data-driven models designed to accurately estimate cotton yield, an important agricultural commodity, can be adopted by farmers, agricultural system modelling experts and agricultural policy-makers in strategic decision-making processes. In this paper a hybrid genetic programing model integrated with the Markov Chain Monte Carlo (MCMC) based Copula technique is developed to incorporate climate-based inputs as the predictors of cotton yield, for selected study regions: Faisalabad (31.4504 °N, 73.1350 °E), Multan (30.1984 °N, 71.4687 °E) and Nawabshah (26.2442 °N, 68.4100 °E), as important cotton growing hubs in the developing nation of Pakistan. Several different types of GP-MCMC-copula models were developed, each with the well-known copula families (i.e., Gaussian, student t, Clayton, Gumble Frank and Fischer-Hinzmann functions) to screen and utilize an optimal cotton yield forecast model for the present study region. The results of the GP-MCMC based hybrid copula model were evaluated with a standalone GP and the MCMC based copula model in accordance with statistical analysis of the predicted yield based on correlation coefficient (r), Willmott's index (WI), Nash-Sutcliffe coefficient (NSE), root mean squared error (RMSE) and mean absolute error (MAE) in the independent test phase. Further performance preciseness was evaluated by the Akiake Information Criterion (AIC), the Bayesian Information Criterion (BIC) and the Maximum Likelihood (MaxL) for the GP-MCMC based copula as well as the MCMC based copula model. GP-MCMC-Clayton copula model generated the most accurate result for the Multan station. For the optimal GP-MCMC-Clayton copula model, the acquired model evaluation metrics for Multan were: (LM≈0.952; RRMSE≈2.107%; RRMAE≈1.771%) followed by the MCMC based Gaussian copula model (LM≈0.895; RRMSE≈4.541%; RRMAE≈0.3.214%) and the standalone GP model (LM≈0.132; RRMSE≈23.638%; RRMAE≈22.652%), indicating the superiority of the GP-MCMC-Clayton copula model in respect to the other benchmark models. The performance of GP-MCMC based copula model was also found to be superior in the case of Faisalabad and Nawabshah station as confirmed by AIC, BIC, MaxL metrics, including a larger value of the Legates-McCabe's (LM) index, utilized in conjunction with the relative percentage RRMSE and the relative mean absolute error (RMAE). Accordingly, it is averred that the developed GP-MCMC copula model can be considered as a pertinent data-intelligent tool used for accurate prediction of cotton yield, utilizing the readily available climate datasets in agricultural regions and is of relevance to agricultural yield simulation and sectoral decision-making.