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Fully Bayesian economically optimal design for a spatially varying coefficient linear stochastic plateau model over multiple years

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Abstract

On-farm experimentation to guide fertilizer recommendations is a potential precision agriculture tool. There is, however, no agreement on the optimal way to conduct on-farm experimentation, which motivated this paper. Optimal on-farm experimentation is addressed using fully Bayesian decision theory. Monte Carlo integration was used, assuming a linear stochastic plateau model with spatially correlated plateau parameters. The spatially varying coefficient model was used to guide the application of site-specific nitrogen. For the Monte Carlo simulation, the true economic optimal nitrogen value was held constant in each plot. Of the designs considered, experimenting on 15 out of 100 plots of a field with treatment levels that were wider than the true optimal levels and with fewer plots at the lowest nitrogen level maximized the farmers' profit over several years. The third year was the best time to quit experimenting. Much current work experiments on the whole field. With a spatially varying coefficient model, much information is gained without experimenting on every plot. The recommended approach is thus to experiment on a few plots scattered throughout the field.

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Notes

  1. The results for 30 percent and 70 percent show similar patterns with roughly the same experimental levels of nitrogen selected and a similar pattern with fewer plots allocated to the low levels of nitrogen.

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Funding

This work was supported by the A.J. and Susan Jacques Chair, the Oklahoma Agricultural Experiment Station, and United States Department of Agriculture National Institute of Food and Agriculture [Hatch Project number OKL03170].

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  1. Department of Agricultural Economics, Oklahoma State University, Stillwater, OK, 74078, USA

    Davood Poursina & B. Wade Brorsen

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  1. Davood Poursina
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All authors contributed to the study conception and design. The computer programs and the first draft of the manuscript were written by DP. All authors commented on previous versions of the manuscript.

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Correspondence to B. Wade Brorsen.

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Poursina, D., Brorsen, B.W. Fully Bayesian economically optimal design for a spatially varying coefficient linear stochastic plateau model over multiple years. Stoch Environ Res Risk Assess 38, 1089–1098 (2024). https://doi.org/10.1007/s00477-023-02615-w

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