On the utility of treating a vineyard against Plasmopara viticola: a Bayesian analysis

Plasmopara viticola is the causal agent of the downy mildew, the most severe disease of grapevines. In order to prevent and/or mitigate the plant disease, fungicide treatments are often required, despite the presence of side effects on the environment and the potential hazard for human health in case of prolonged exposition. The choice of proper treatments and optimal scheduling is the key to managing downy mildew in an eco-friendly way. Plasmopara viticola’s growth depends on meteorological variables, like temperature and rain, plant’s genotype, the degree of exposition to oospores and soil conditions. Field measurements are expensive both for the high cost of oospore sensors and for the need of meteorological sensors describing the microclimate around each plant. Whatever the amount of information gathered from sensors of a vineyard, a decision must be taken, e.g. according to the predicted probability of infected leaves (and grapes) and considering side effects like the impact of a chemical treatment on the soil and on biodiversity. A multi-attribute utility function on variables describing future consequences of a decision may be defined by following the assumptions of utility independence and preferential independence. The inherent uncertainty is described by a Bayesian prior-predictive distribution where prior are elicited from experts, and eventually updated using available data. The resulting optimal decision is defined as the argument that maximises the expected value of the utility function. The proposed utility function may be tuned to match the individual preference scheme of the winegrower and eventually extended to include further variables like those describing the quality and yield of grapes.