### Abstract

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 language | English (US) |
---|---|

Pages (from-to) | 291-305 |

Number of pages | 15 |

Journal | Stochastic Environmental Research and Risk Assessment |

Volume | 17 |

Issue number | 5 |

DOIs | |

State | Published - Nov 2003 |

### Fingerprint

### Keywords

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

### ASJC Scopus subject areas

- Environmental Engineering
- Environmental Science(all)
- Environmental Chemistry
- Water Science and Technology
- Statistics and Probability
- Civil and Structural Engineering

### Cite this

**Maximum likelihood Bayesian averaging of uncertain model predictions.** / Neuman, Shlomo P.

Research output: Contribution to journal › Article

}

TY - JOUR

T1 - Maximum likelihood Bayesian averaging of uncertain model predictions

AU - Neuman, Shlomo P

PY - 2003/11

Y1 - 2003/11

N2 - 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.

AB - 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.

KW - Bayesian averaging

KW - Conceptual modeling

KW - Maximum likelihood

KW - Model structure

KW - Uncertainty

UR - http://www.scopus.com/inward/record.url?scp=0348225037&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0348225037&partnerID=8YFLogxK

U2 - 10.1007/s00477-003-0151-7

DO - 10.1007/s00477-003-0151-7

M3 - Article

AN - SCOPUS:0348225037

VL - 17

SP - 291

EP - 305

JO - Stochastic Environmental Research and Risk Assessment

JF - Stochastic Environmental Research and Risk Assessment

SN - 1436-3240

IS - 5

ER -