Maximum likelihood Bayesian averaging of uncertain model predictions

S. P. Neuman

Research output: Contribution to journalArticlepeer-review

336 Scopus citations


Hydrologic analyses typically rely on a single conceptual-mathematical model. Yet hydrologic environments are open and complex, rendering them prone to multiple interpretations and mathematical descriptions. Adopting only one of these may lead to statistical bias and underestimation of uncertainty. A comprehensive strategy for constructing alternative conceptual-mathematical models of subsurface flow and transport, selecting the best among them, and using them jointly to render optimum predictions under uncertainty has recently been developed by Neuman and Wierenga (2003). This paper describes a key formal element of this much broader and less formal strategy that concerns rendering optimum hydrologic predictions by means of several competing deterministic or stochastic models and assessing their joint predictive uncertainty. The paper proposes a Maximum Likelihood Bayesian Model Averaging (MLBMA) method to accomplish this goal. MLBMA incorporates both site characterization and site monitoring data so as to base the outcome on an optimum combination of prior information (scientific knowledge plus data) and model predictions. A preliminary example based on real data is included in the paper.

Original languageEnglish (US)
Pages (from-to)291-305
Number of pages15
JournalStochastic Environmental Research and Risk Assessment
Issue number5
StatePublished - Nov 2003


  • Bayesian averaging
  • Conceptual modeling
  • Maximum likelihood
  • Model structure
  • Uncertainty

ASJC Scopus subject areas

  • Environmental Engineering
  • Environmental Chemistry
  • Safety, Risk, Reliability and Quality
  • Water Science and Technology
  • Environmental Science(all)


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