Geodesic
Goal-oriented adaptive sampling under random field modelling of response probability distributions
Athénaïs Gautier1 ; David Ginsbourger1 ; Guillaume Pirot2
1 Institute of Mathematical Statistics and Actuarial Science, University of Bern, Switzerland
2 Centre for Exploration Targeting, The University of Western Australia, Australia
ESAIM. Proceedings, Tome 71 (2021), pp. 89-100.

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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.
DOI : 10.1051/proc/202171108

Athénaïs Gautier 1 ; David Ginsbourger 1 ; Guillaume Pirot 2

1 Institute of Mathematical Statistics and Actuarial Science, University of Bern, Switzerland
2 Centre for Exploration Targeting, The University of Western Australia, Australia 
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     title = {Goal-oriented adaptive sampling under random field modelling of response probability distributions},
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Athénaïs Gautier; David Ginsbourger; Guillaume Pirot. Goal-oriented adaptive sampling under random field modelling of response probability distributions. ESAIM. Proceedings, Tome 71 (2021), pp. 89-100. doi : 10.1051/proc/202171108. http://geodesic.mathdoc.fr/articles/10.1051/proc/202171108/

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