New paper in Mathematical Geosciences to start 2019, showcasing the work of Felipe Santibanez, Ph. D. student at Universidad de Chile, in collaboration with Prof. Jorge Silva. You can download it here.

## Sampling Strategies for Uncertainty Reduction in Categorical Random Fields: Formulation, Mathematical Analysis and Application to Multiple-Point Simulations

**Felipe Santibañez **(Information and Decision System Group (IDS), Department of Electrical Engineering, University of Chile), **Jorge F. Silva **(Information and Decision System Group (IDS), Department of Electrical Engineering, University of Chile), **Julian M. Ortiz **(The Robert M. Buchan Department of Mining, Queen’s University)

**Abstract**

The task of optimal sampling for the statistical simulation of a discrete random

field is addressed from the perspective of minimizing the posterior uncertainty of non-sensed positions given the information of the sensed positions. In particular, information theoretic measures are adopted to formalize the problem of optimal sampling design for field characterization, where concepts such as information of the measurements, average posterior uncertainty, and the resolvability of the field are introduced. The use of the entropy and related information measures are justified by connecting the task of simulation with a source coding problem, where it is well known that entropy offers a fundamental performance limit. On the application, a one-dimensional Markov chain model is explored where the statistics of the random object are known, and then the more relevant case of multiple-point simulations of channelized facies fields is studied, adopting in this case a training image to infer the statistics of a nonparametric model. In both contexts, the superiority of information-driven sampling strategies is proved in different settings and conditions, with respect to random or regular sampling.