This thesis addresses the critical challenge of predicting crop yield. As the demand for food surges due to population growth, accurate and efficient predictive models become increasingly important. Leveraging a comprehensive database from the Horizon 2020 InnoVar project, which includes variables across phenomics, genomics, soil, and weather conditions, we aim to extend the existing Additive Main Effects and Multiplicative Interaction (AMMI) modelling framework. Our work is divided into three key contributions. First, we propose a computationally efficient Bayesian AMMI model using variational inference, addressing the high computational costs often associated with traditional Markov chain Monte Carlo methods. Second, we introduce the Bayesian Additive Main effects and Multiplicative Interaction Tensor (BAMMIT) model, which extends the AMMI model to accommodate multiple categorical variables. Third, we present the Clustered Bayesian Additive Main Effects and Multiplicative Interaction Tensor (CBAMMIT) model, incorporating Gaussian Mixture Models to allow for the inclusion of categorical representations of numerical variables. Our findings show that these extensions not only improve predictive accuracy but also offer probabilistic assessments of predictions. They have real-world applicability, as demonstrated using data from Ireland, and can potentially guide stakeholders in agriculture – from farmers to policymakers – in making informed decisions.