Goal-oriented adaptive sampling under random field modelling of response probability distributions

In the study of natural and artificial complex systems, responses that are not completely determined by considered decision variables commonly modelled probabilistically, resulting in response distributions varying across space. We consider cases where spatial variation these does only concern their mean and/or variance but also other features including for instance shape or uni-modality versus multi-modality. Our contributions build upon a non-parametric Bayesian approach to modelling thereby induced fields probability distributions, particular extension logistic Gaussian model. The models deliver probabilistic predictions at candidate points, allowing perform (approximate) posterior simulations density functions, jointly predict multiple moments functionals target as well quantify impact collecting new samples on state knowledge distribution field interest. particular, we introduce adaptive sampling strategies leveraging potential random guide system evaluations goal-oriented way, with view towards parsimoniously addressing calibration related problems from non-linear (stochastic) inversion global optimisation.