<p>Fault detection and diagnosis in wind turbines is important for economic and reliability reasons. Existing studies for fault detection mostly detect if a fault exists or not without diagnosing its magnitude and type, or quantifying the uncertainty therein. We complement existing works with Bayesian regression approaches that estimate the complete probability distributions of different types of faults in wind turbine rotor speed sensor and pitch actuator. We use Markov Chain Monte Carlo methods to infer fault distributions using the true inputs to the sensor or actuator, estimated using rotor dynamics models, and the observed faulty values. As a baseline for our model-based methods, we develop a pure data-driven binary classifier for fault detection. Using simulated wind turbine data, we show that our model-based Bayesian approaches outperform the baseline by giving an at least 7% higher Area Under Precision Recall Curve for fault detection. Through a fault tolerant pitch control scheme in software, we show the energy improvement from our inference methods to be within at most 57% of the ideal energy output possible with a complete fault repair in hardware.</p>