Nonparametric Bayesian Modeling: An Introduction to Gaussian Processes with PyMC

Gaussian Processes (GPs) are flexible tools for Bayesian nonparametric modeling, providing an effective solution for nonlinear regression and classification problems where traditional parametric models often fail due to assumptions about functional form or error distribution. GPs model the underlying function directly, defining a distribution over functions that inherently yields robust, probabilistic predictions and uncertainty quantification. This course offers a practical introduction, starting with core Bayesian concepts and a concise PyMC tutorial. We will explore how to specify models using covariance functions (kernels) and apply both Marginal (conjugate) and Latent (non-conjugate) GPs to real-world data. The course culminates in building complex structures, such as additive and multiplicative kernels and hierarchical models, and addresses the critical issue of scalability. Attendees will learn when and how to deploy efficient modern approximations, such as the Hilbert Space Gaussian Process (HSGP), necessary for applying GPs to larger datasets. **Prerequisite Knowledge**: Learners should have familiarity with basic statistical modeling (e.g., linear regression, estimation) and core components of the scientific Python stack (NumPy, pandas, Jupyter). No direct experience with PyMC or Bayesian statistics is expected.