Representative Consensus from Limited-Size Ensembles

Abstract

Characterizing the uncertainty and extracting reliable visual information from ensemble data have been persistent challenges in various disciplines, specifically in simulation sciences. Many ensemble analysis and visualization techniques take a probabilistic approach to this problem with the assumption that the ensemble size is large enough to extract reliable statistical or probabilistic summaries. However, many real-life ensembles are rather limited in size, with only a handful of members, due to various restrictions such as storage, computational power, or sampling limitations. As a result, probabilistic inference is subject to imprecision and can potentially result in untrustworthy information in the presence of a limited sample-size ensemble. In this case, a more reliable approach is to fuse the information present in an ensemble with a limited number of members with minimal assumptions. In this paper, we propose a technique to construct a representative consensus that is particularly suited for ensembles of a relatively small size. The proposed technique casts the problem as an ordering problem in which at each point in the domain, the ensemble members are ranked based on the local neighborhood. This local approach allows us to provide shape and irregularity sensitivity. The local order statistics will then be fused to construct a global consensus using a Bayesian approach to ensure spatial coherency of the local information. We demonstrate the utility of the proposed technique using a synthetic and two real-life examples.