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

TL;DR

This paper develops a non-parametric Bayesian model for spatially varying response distributions in complex systems, enabling goal-oriented adaptive sampling for efficient system evaluation and calibration.

Contribution

It introduces a spatial extension of the logistic Gaussian model for response distribution fields and adaptive sampling strategies based on these models.

Findings

Effective probabilistic predictions of response distributions across decision space.

Ability to perform posterior simulations and predict multiple distribution functionals.

Guidance for system evaluations in calibration and optimization tasks.

Abstract

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