Accurate and timely predictions of grape yield are required by the wine industry for logistics planning, crop management, and wine marketing strategies. The Grape Yield Analyser project is an interdisciplinary collaboration aiming to predict grape yield in a timely and efficient manner. A Bayesian growth model assuming a double sigmoidal curve has been developed by ellis to predict grape yield. The model requires measurements of grape bunch mass at different times during the growing season. Such measurements require substantial trained staff and are also time-consuming and destructive. Hence, there is increasing research into the use of sensors in the industry. Since most sensors do not directly measure the mass of grape bunches, it can be difficult to obtain precise measurements of the grape bunch weights.

In this thesis, we provide the modelling framework for incorporating sensor-based measurements into the existing growth model. We assume the sensors produce measurements of grape bunch mass with known uncertainties. We present models which can incorporate uncertainties in continuous response variables and produce accurate (unbiased) and precise (minimal variability) predictions. MCMC algorithms are provided to estimate the proposed models for the two situations: (i) when the uncertainty is reported in the form of a parametric distribution, and (ii) when the uncertainty is reported in the form of a sample of values representing a nonparametric distribution.

We use simulation studies to evaluate the resulting model. In the first situation, our Bayesian model which incorporates uncertainty assuming a normal error distribution can perform well when the uncertainty is smaller than 80% of the population variation. In the second situation, when we have a sample of values representing a nonparametric distribution instead of a precise measurement, a naïve analysis can still produce accurate and precise measurements, given that the sample mean is an unbiased estimator of the actual value and for a large enough sample size. The models in this thesis can be applied to regression problems in other fields, such as chemistry, medicine and physics, when there are continuous response variables reported with uncertainties.