Thinking Bayesian for Plasma Physicists*

Bayesian statistics is a powerful tool for making inferences about the physical world based on data. It is particularly well-suited for scientific applications, as it naturally treats everything as a probability. This perspective allows for uncertainty quantification, incorporation of prior knowledge, and robustness to ill-posed problems. This tutorial introduces key concepts that have practical applications in plasma physics. The tutorial begins with a simple, non-technical example that defines terms and general concepts in an intuitive manner. It then progresses to the common problem of linear regression, explaining how a Bayesian approach can enhance the traditional perspective. Following this, curve fitting using Gaussian Process Regression (GPR) is introduced, with examples of fitting Thomson measurement of electron temperature and density profiles in both Low- and High-(Confinement)-Mode tokamak plasmas. Bayesian statistics has contributed significantly to recent advancements in machine learning (ML). This tutorial demonstrates how addressing uncertainty in ML provides insights into optimizing ML models and determining when their inferences should not be trusted. Finally, a brief discussion on the application of Bayesian statistics to inverse problems is presented including important tokamak profile and other data analysis applications.