Antimicrobial resistance (AMR) is the ability of an infection to stop antimicrobials, such as antibiotics, antivirals and antimalarials, from working against it. In the EU, every year AMR is responsible for thousands of deaths and costs millions of euros. Yet forecasting the prevalence of AMR remains an open challenge. This project meets this challenge by developing cutting-edge Hierarchical Bayesian models (HBMs). As a case study, the models will focus on the malaria parasite Plasmodium falciparum that has developed resistance to sulfadoxine/pyrimethamine between 1994 and 2016. This ensures that the goals are realistic, with immediate insight and impact, whilst also remaining methodologically relevant for all AMR. Within the field of ecology, regression models are being replaced so as to incorporate more complex non-linear relationships between abundance and the environment. Unlike traditional methods, HBMs are spatiotemporal models that (i) account for varying geography (ii) separate underlying processes and (iii) include uncertainty in the data and model parameters. This thorough package has proven to yield more insight and accuracy. By using partial differential equations, HBMs separate occurrence due to spread and occurrence due to emergence. Despite its relevance, differentiating between these two process is currently unexplored in epidemiology. Furthermore, when modelling AMR, infections competing for hosts is a process which is currently unexplored in HBMs. Thus, the two long term contributions of this project are: Bringing HBMs to epidemiology to gain a better understanding of underlying processes, and advancing the field of HBMs to include more complex dynamics. And more immediately, the two key contributions are: Quantifying the dynamics and influencers of the spread of drug resistant malaria, and forecasting the frequency of partially drug resistant malaria, and fully drug resistant malaria, at different locations and at different times.