Statistical inference provides both predictions and quantification of uncertainty, typically expressed in terms of confidence or credible intervals that are expected to contain the quantity of interest, such as the support of a political party, "with high probability". We study how prior assumptions encoded in a Gaussian process model affect the reliability of uncertainty quantification in Bayesian statistical inference. For example, if one assumes that the truth is much smoother (i.e., that observations at two nearby sensor locations are quite similar) than it really is, the model may end up becoming overconfident: The credible intervals are much narrower than they should be and unlikely to contain the truth. Overconfidence may have serious repercussions in subsequent decision-making. In this project we will develop both a mathematical theory for the reliability of Gaussian process models under misspecification and new computational methods that work even if the model is misspecified.

2025

2029