Gaussian Processes from First Principles

Gaussian process regression, classification, and count models with explicit covariance kernels, exact Gaussian inference, Laplace approximations for non-Gaussian likelihoods, sparse approximations, marginal-likelihood optimization, derivatives, posterior sampling, calibration diagnostics, and time-series workflows. The implementation follows the core methodology of Rasmussen and Williams (2006) and emphasizes numerical stability, transparent assumptions, and reproducible statistical workflows.