Theory Manual# Gaussian Processes# Contents: Gaussian Processes Making Predictions Posterior Predictive Distribution Learning Hyperparameters Computational Considerations Derivative-Enhanced Gaussian Processes Hessian-Enhanced Gaussian Processes Note on Simplified Test Predictions Derivative Screening Weighted Gradient Enchanced Gaussian Processes Problem Formulation Submodel Covariance Structure Weighted Combination of Submodels Computing Weight Functions Hyperparameter Optimization Computational Trade-offs References Directional Derivative-Enhanced Gaussian Processes Covariance Structure Hyperparameter Optimization Computational Advantages References Multi-output Gaussian Processes A Note on DEGPs References Gradient Enhanced Multi-output Gaussian Processes Note on Observation Noise Noisy Joint Distribution Noisy Posterior Noisy Marginal Log-Likelihood Generalization Heteroscedastic Noise