# Frontiers of Earth Science

 REVIEW |
Ensembles vs. information theory: supporting science under uncertainty
Grey S. NEARING1, Hoshin V. GUPTA2()
1. University of Alabama, Department of Geological Sciences, Tuscaloosa, AL 35294-1152, USA
2. University of Arizona, Department of Hydrology and Atmospheric Sciences, Tucson, AZ 85721-0158, USA
 Download: PDF(168 KB)   HTML Export: BibTeX | EndNote | Reference Manager | ProCite | RefWorks
 Abstract Multi-model ensembles are one of the most common ways to deal with epistemic uncertainty in hydrology. This is a problem because there is no known way to sample models such that the resulting ensemble admits a measure that has any systematic (i.e., asymptotic, bounded, or consistent) relationship with uncertainty. Multi-model ensembles are effectively sensitivity analyses and cannot – even partially – quantify uncertainty. One consequence of this is that multi-model approaches cannot support a consistent scientific method – in particular, multi-model approaches yield unbounded errors in inference. In contrast, information theory supports a coherent hypothesis test that is robust to (i.e., bounded under) arbitrary epistemic uncertainty. This paper may be understood as advocating a procedure for hypothesis testing that does not require quantifying uncertainty, but is coherent and reliable (i.e., bounded) in the presence of arbitrary (unknown and unknowable) uncertainty. We conclude by offering some suggestions about how this proposed philosophy of science suggests new ways to conceptualize and construct simulation models of complex, dynamical systems. Corresponding Authors: Hoshin V. GUPTA Just Accepted Date: 08 April 2018   Online First Date: 09 May 2018
 Cite this article: Grey S. NEARING,Hoshin V. GUPTA. Ensembles vs. information theory: supporting science under uncertainty[J]. Front. Earth Sci., 09 May 2018. [Epub ahead of print] doi: 10.1007/s11707-018-0709-9. URL: http://journal.hep.com.cn/fesci/EN/10.1007/s11707-018-0709-9 http://journal.hep.com.cn/fesci/EN/Y/V/I/0
 Fig.1  Diagram of a simple experiment with a single input and single output. Even in the simplest case, we require at least one process hypothesis $ℏ p$, and at least two measurement models $ℏu$ and $ℏy$. Aleatory uncertainty is defined as the (unknown) distribution $&(zy |zu)$, which would only be knowable if we had access to both a perfect process model and also perfect measurement models. A full model is the conjunction $ℏ= {ℏp, ℏu , ℏ y}$.