Using Monte Carlo method for parameter estimation and fertilization recommendation of multivariate fertilizer response model

Multivariate fertilizer response models are often non–representative models for recommending fertilization. The Monte Carlo’s principle and its applications for estimating parameters of multivariate fertilizer response models, and for fertilization recommendation method of non–representative models were studied using the ‘3414’ field fertilizer experiment design. About 67 two-nutrients and 59 three-nutrient second degree polynomial models are developed using the least square method. Among these models, the representative fertilizer response models only account 23.1% and 16.9%, respectively. While the rates increased to 56.7% and 37.3% by using the Monte Carlo method to estimate the model parameters. Compared to the least square method, the Monte Carlo method may obtain the best parameters in plant nutrition and fitting sum of square in error mathematically by abandoning properly best character in sum of square in error in the least square method. Therefore, the rates are increased. As a case in this study, there is a non–representative PK duality model which adopts the least squares method or even the Monte Carlo method to estimate their parameters. Using yield frequency analysis to recommend fertilization, only a group of P and K coenobium, the sixth treatment, meets the conditions of goal yield. It stands that the coenobium number is not enough as a basis for fertilization recommendation, and results in the P recommending application rate on the high side and K on the low side. Under the same goal yield, the Monte Carlo method may obtain the average P and K recommending application amounts which are within the P and K optimum application rates based on NP, NK and NPK multivariate representative models in the same experiment sites. These results are obvious better than those of yield frequency analysis method. Therefore, the Monte Carlo method provides a new technique to estimate parameters and fertilization recommendation for multivariate fertilizer response models.