Advancing our understanding of the connections among groundwater, food, and climate is critical to meet global food demands while optimizing water resources usage. However, our understanding of the linkages among groundwater, food, and climate is still limited. Here, we offer a Bayesian framework to simulate crop yield at a regional scale and quantify its relationships and associated uncertainty with climate, groundwater, agricultural, and energyrelated variables. We implemented the framework in the rice-producing regions of Louisiana from 1960-2015. To build a parsimonious model, we used a probability-based variable selection approach to detect the key drivers of rice yield. Rice yield increased, groundwater declined, and area planted declined or did not change over 56yrs. The number of irrigation wells, groundwater level, air temperature, and area planted were found to be the key drivers of rice yield. The regression coefficients showed that rice yield was positively related to groundwater level, and negatively related to area planted and the number of irrigation wells. The limited influence of N fertilizer was noted on rice yield for the period when fertilizer data were available. The inverse relationship between rice yield and area planted pointed to the adaption of efficient crop management practices that maintained or increased yield, despite the decline in area planted. The farmers' ability to install irrigation wells during droughts sustained the yields over long-term but not short-term. This decline in rice yield in response to drought over the short-term might explain the negative relation between yield and irrigation wells. Overall, this work highlighted the uncertainty in relationships between rice yield and key drivers and quantified the intimate connection between food and groundwater. This work may have implications for managing two highly competing commodities (i.e., groundwater and food) in agricultural regions.