Bridging the gap between GLUE and formal statistical approaches: approximate Bayesian computation

By Mojtaba Sadegh, Jasper A. Vrugt. 2013

67 citations recorded by the source corpus.

In recent years, a strong debate has emerged in the hydrologic literature regarding how to properly treat nontra- ditional error residual distributions and quantify parameter and predictive uncertainty. Particularly, there is strong dis- agreement whether such uncertainty framework should have its roots within a proper statistical (Bayesian) context using Markov chain Monte Carlo (MCMC) simulation techniques, or whether such a framework should be based on a quite dif- ferent philosophy and implement informal likelihood func- tions and simplistic search methods to summarize parame- ter and predictive distributions. This paper is a follow-up of our previous work published in Vrugt and Sadegh (2013) and demonstrates that approximate Bayesian computation (ABC) bridges the gap between formal and informal statis- tical model-data fitting approaches. The ABC methodology has recently emerged in the fields of biology and population genetics and relaxes the need for an explicit likelihood func- tion in favor of one or multiple different summary statistics that measure the distance of each model simulation to the data. This paper further studies the theoretical and numerical equivalence of formal and informal Bayesian approaches us- ing discharge and forcing data from different watersheds in the United States, in particular generalized likelihood uncer- tainty estimation (GLUE). We demonstrate that the limits of acceptability approach of GLUE is a special variant of ABC if each discharge observation of the calibration data set is used as a summary diagnostic.

Subfields: Artificial Intelligence, Environmental Engineering, Water Science and Technology

View Paper: https://www.semanticscholar.org/paper/97de64304586c05949f144a957cda17274f59c76

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Artificial Intelligence

1. Keith Beven
2. Jasper A. Vrugt
3. Mojtaba Sadegh
4. Patrick M. Reed
5. Jirka Šimůnek
6. David Hadka

In Environmental Engineering

1. Jasper A. Vrugt
2. Mojtaba Sadegh
3. Keith Beven
4. Chonggang Xu
5. E. Volpi
6. Hoshin V. Gupta
7. M. Clark
8. Ming Ye

In Water Science and Technology

1. Jasper A. Vrugt
2. Mojtaba Sadegh
3. Keith Beven
4. Chonggang Xu
5. E. Volpi
6. Hoshin V. Gupta
7. Ming Ye
8. M. Clark

Citations in the corpus

• The stationarity paradigm revisited: Hypothesis testing using diagnostics, summary metrics, and DREAM(ABC) (2015, background): “…a randomly sampled solution will fall exactly within the hypercube defined by (see Figure 4) is disturbingly small, particularly if the prior parameter distribution is large compared to the behavioral (posterior) solution space and the number of summary metrics is large [Sadegh and Vrugt, 2013].”
• Facets of uncertainty: epistemic uncertainty, non-stationarity, likelihood, hypothesis testing, and communication (2016, background): “…likelihood measures or limits of acceptability might be justified (e.g. within the GLUE framework of Beven 2006a, 2012, Beven and Binley 1992, 2014, Freer et al. 2004, Smith et al. 2008, Liu et al., 2009; and within approximate Bayesian computation by Nott et al. 2012, Sadegh and Vrugt 2013, 2014).”