基于贝叶斯理论的小麦籽粒镉铅超标风险预测

对农作物污染风险进行预测具有重大意义.基于贝叶斯定理及数据分布特征，建立了贝叶斯风险预测模型，并使用区域大田调查土壤-小麦重金属含量数据，预测小麦籽粒Cd和Pb超标风险并验证该模型的准确度.结果表明，该模型预测小麦籽粒Cd超标风险时相对偏差较小，以小麦籽粒Cd含量为变量的预测相对偏差仅为(2.66±1.87)%,以土壤DTPA-Cd含量和土壤Cd全量为变量时预测相对偏差则分别为(5.11±3.77)%和(5.88±3.87)%, 3个变量均能使预测结果与真实超标概率的平均相对偏差小于10%.预测小麦籽粒Pb超标风险时，仅小麦籽粒Pb含量的预测相对偏差小于10%.数据来源、数据分布特征和变量的选择是影响贝叶斯风险预测模型预测相对偏差的重要因素.该模型基于大田数据的先验分布，能够有效反映大田生产条件下小麦籽粒重金属与土壤因子间的相互关系，预测较准确，具有应用潜力.

Risk Prediction of Cadmium and Lead in Wheat Grains Based on Bayes Theorem

Wheat plants have been reported to accumulate high concentrations of potentially toxic trace elements such as cadmium (Cd) and lead (Pb). Such Cd-contaminated wheat grains present serious public health challenges for local populations in China. Therefore, it is necessary to establish a risk forewarning method for the accumulation of Cd and Pb in wheat grain caused by contaminated soils. In this study, a Bayesian risk prediction model was established based on Bayes theorem and the dataset from field investigations. The results indicated that the proposed model could accurately predict the probability of the concentration of Cd in wheat grain exceeding the national safety limit. The concentration of Cd in rice grain could be better estimated by using the soil total Cd, DTPA extractable Cd, and wheat grain Cd as the variables, with their predicted deviations of (5.88±3.87)%, (5.11±3.77)%, and (2.66±1.87)%, respectively. Only the Pb in wheat grain showed better results with a low predicted deviation value of (8.06±5.52)%. Soil total Pb and DTPA-Pb were not suitable for predicting the standard-exceeding risk of wheat grain Pb, with deviations of (12.8±8.05)% and (13.8±7.09)%, respectively. The data source, data distribution characteristics, and selected variables were the key factors affecting the prediction accuracy of the Bayesian risk prediction model. Similar distributions of the prior and posterior data and high correlation coefficients between the soil variables and the concentrations of heavy metals in the wheat grain contents contributed to the minimization of model uncertainty. The proposed Bayesian risk prediction model was reliable and did not lead to over- or under-conservative predictions of the pollution of Cd and Pb in wheat grain caused by contaminated soils, which could be also extended to cover other contaminants and contaminated areas.