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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?

Lefty
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  • I am not sure to understand your question. A confidence interval is a distribution. – Thomas Schillaci Mar 06 '20 at 08:30
  • @ThomasSchillaci Confidence intervals are point estimates and they differ from the Credible intervals (where you can talk about probabilities) https://en.wikipedia.org/wiki/Credible_interval – Lefty Mar 06 '20 at 08:48
  • I have to disagree with this, confidence intervals are intervals computed from your data. I think, this clarification would be more suited on cross validated https://stats.stackexchange.com/ – Thomas Schillaci Mar 06 '20 at 08:53

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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

max0r
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