Designing wind-to-power (W2P) models is a discipline within the wind turbine industry where the produced power from wind turbine generators is modelled as a function of wind. The current regime of W2P models is data-driven where models are made with little to no regard as to the physical phenomena at play. This thesis investigates how to design a W2P model directly based on the physical processes of a wind turbine using statistical modelling of wind speed available as prior information for a specific site. The statistics are based on the method/design philosophy Approximate Bayesian Total Error Analysis developed for this thesis. Markov Chain Monte Carlo methods have been used to infer model parameters. Two different models, the AW2P and NTF-AW2P model are designed and compared to existing models in a performance evaluation. The two models show similar performance but perform similarly or worse compared to existing W2P models across several error measurements, thus further research is needed to improve the models.