Posterior Consistency for Gaussian Process Surrogate Models with Generalized Observations

Gaussian processes (GPs) are widely used as approximations to complex computational models. However, properties and implications of GP approximations on data analysis are not yet fully understood. In this work we study parameter inference in GP surrogate models that utilize generalized observations, and prove conditions and guarantees for the approximate parameter posterior to be consistent in terms of posterior expectations and KL-divergence.