Gaussian Process Confidence vs Credible Intervals

Question

Since Gaussian Process returns a distribution and not a point estimate, why this example (and actually in every example with GP) talk about Confidence Intervals on the analogues for Bayesian statistics the Credible Intervals?

Answer 1

I was wondering about that, too. My assumption is the following: GaussianProcessRegressor from sklearn implements Algorithm 2.1 from Rasmussen & Williams (2006). Throughout this book, the ±2σ interval around µ is referred to as "95% confidence region". They simply do not make a distinction between "confidence" and "credible" region. I think the authors of sklearn adopted that.

C. E. Rasmussen & C. K. I. Williams, Gaussian Processes for Machine Learning, MIT Press, 2006