Generalizing the derivation of the schwarz information criterion

Cavanaugh, Joseph E.; Neath, Andrew A.

doi:10.1080/03610929908832282

Cited by 102 publications

(75 citation statements)

References 37 publications

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“…Novel techniques for efficient parameter uncertainty estimation, data assimilation, numerical integration, and multimodel ensemble prediction have been introduced to better describe or tame hydrological prediction uncertainty [such as Vrugt et al, 2009;Moradkhani et al, 2005;Kavetski and Clark, 2010;Parrish et al, 2012]. Bayesian approaches to hydrological model selection, prediction uncertainty, model complexity, and regularization have also been well studied [Schwarz, 1978;Jakeman and Hornberger, 1993;Young et al, 1996;Cavanaugh and Neath, 1999;Ye et al, 2008;Gelman et al, 2008]. The use of prior distribution as a regularization term in a log-likelihood maximization is similar in form to the regularization proposed in this paper [Gelman et al, 2008].…”

Section: Introductionmentioning

confidence: 99%

“…The use of prior distribution as a regularization term in a log-likelihood maximization is similar in form to the regularization proposed in this paper [Gelman et al, 2008]. Ye et al [2008] compared AIC, BIC, and KIC measures and showed that an effective complexity measure (and thus regularization based on it) in KIC, being a finite (though asymptotically large) sample version of BIC [Ye et al, 2008], depends on the Hessian of the likelihood function at the optimum under certain regularity conditions [Cavanaugh and Neath, 1999;Ye et al, 2008]. Meanwhile in BIC it depends on model parameter dimensionality.…”

Section: Introductionmentioning

confidence: 99%

“…The regularity conditions are used to replace the need for full specification (that the observations are generated by a member of the model space specified by a likelihood function). These conditions exploit the second-order Taylor series expansion of a log-likelihood function, certain assumptions on the prior and large sample size arguments to justify the use of KIC for model selection [Cavanaugh and Neath, 1999]. The use of KIC for model selection may however not be accurate for finite sample sizes.…”

Section: Introductionmentioning

confidence: 99%

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On hydrological model complexity, its geometrical interpretations and prediction uncertainty

Arkesteijn

Pande

2013

Water Resour. Res.

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[1] Knowledge of hydrological model complexity can aid selection of an optimal prediction model out of a set of available models. Optimal model selection is formalized as selection of the least complex model out of a subset of models that have lower empirical risk. This may be considered equivalent to minimizing an upper bound on prediction error, defined here as the mathematical expectation of empirical risk. In this paper, we derive an upper bound that is free from assumptions on data and underlying process distribution as well as on independence of model predictions over time. We demonstrate that hydrological model complexity, as defined in the presented theoretical framework, plays an important role in determining the upper bound. The model complexity also acts as a stabilizer to a hydrological model selection problem if it is deemed ill-posed. We provide an algorithm for computing complexity of any arbitrary hydrological model. We also demonstrate that hydrological model complexity has a geometric interpretation as the size of model output space. The presented theory is applied to quantify complexities of two hydrological model structures: SAC-SMA and SIXPAR. It detects that SAC-SMA is indeed more complex than SIXPAR. We also develop an algorithm to estimate the upper bound on prediction error, which is applied on five different rainfall-runoff model structures that vary in complexity. We show that a model selection problem is stabilized by regularizing it with model complexity. Complexity regularized model selection yields models that are robust in predicting future but yet unseen data.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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On hydrological model complexity, its geometrical interpretations and prediction uncertainty

Arkesteijn

Pande

2013

Water Resour. Res.

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“…BIC (equation 3) was derived in a Bayesian context by Schwarz (1978) as an asymptotic approximation to a transformation of the posterior probability of a candidate model (Cavanaugh and Neath, 1999). BIC is similar in form to AIC and AICc:…”

Section: Model Selection Criteriamentioning

confidence: 99%

Characterizing regional groundwater flow in the Ethiopian Rift: A multimodel approach applied to Gidabo River Basin

Mechal¹,

Birk²,

Winkler³

et al. 2016

AJES

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Being located in the tectonically active Ethiopian Rift, the hydrogeology of the Gidabo River Basin is complex due to the disruption of lithologies by faults and the variability and lateral discontinuity of the aquifers. Hydrogeochemical and isotopic data suggest that the aquifers within the rift floor receive a relevant contribution of groundwater recharged in the highland. However, the incomplete knowledge about the aquifer properties, the hydraulic behavior of the faults, and the boundary conditions cause uncertainties in this conceptual hydrogeological model. To account for these uncertainties fourteen different numerical models with a stepwise increase from 7 to 40 adjustable parameters were developed, calibrated against the same hydraulic head observations, and ranked according to the Akaike information criteria (AIC and AICc) and Bayesian information criterion (BIC). Based on the information criteria five plausible models were identified, all of which were successfully verified against the river baseflow. The highest likelihood is attributed to a model with eleven adjustable parameters that does not explicitly account for the fault zones; other plausible models considering faults as semi-barriers achieve a slight improvement in model fit but have lower likelihood due to the increased number of calibration parameters. Thus, the effect of faults on groundwater flow needs further investigation, particularly at a local scale.On a regional scale, the hydraulic head distributions of the plausible models agree reasonably well with the equipotential map interpolated from well observations. The estimated transmissivity values range between 30 m 2 / day and 1350 m 2 / day and generally increase from the mountains towards the rift floor. The water budget shows that 75 % of the groundwater recharge supplies baseflow to the rivers. The remaining water infiltrates to the deeper aquifers where less than 1 % is abstracted by pumping wells and the rest flows towards Lake Abaya. Within the rift floor, the majority of inflow to the aquifers is from direct recharge; nevertheless, 35 % of the inflow is contributed by mountain block recharge (lateral groundwater flow from the escarpment and highland). The results of this study strongly advocate the idea to incorporate alternative plausible models instead of relying on single models in the practice of groundwater modeling especially in areas of complex hydrogeology and limited data availability.Die Hydrogeologie des im tektonisch aktiven Äthiopischen Graben gelegenen Gidabo-Flusseinzugsgebiets ist aufgrund der störungs bedingten Unterbrechungen der Lithologien sowie der Variabilität und lateralen Diskontinuität der Aquifere komplex. Hydro geochemische und Isotopen-Daten weisen darauf hin, dass in den Aquiferen der Grabensohle ein relevanter Beitrag von Grundwässern vorliegt, die im Hochland neugebildet werden. Die unvollständige Kenntnis der Aquifereigenschaften, der hydraulischen Wirkung der Störungen und der Randbedingungen führen jedoch zu Unsicherheiten in diesem ko...

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“…(See Al-Saubaihi (2007)). Cavanaugh (1999), proposed a new class of criterion for linear model selection denoted by KIC, KIC C , and MKIC as analogue to AIC, AIC C , MAIC respectively. He illustrated its performance in a simulation study for choosing an order of autoregression.…”

Section: Introductionmentioning

confidence: 99%

New Criteria of Model Selection and Model Averaging in Linear Regression Models

Haggag

2014

AJTAS

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Abstract:Model selection is an important part of any statistical analysis. Many tools are suggested for selecting the best model including frequentist and Bayesian perspectives. There is often a considerable uncertainty in the selection of a particular model to be the best approximating model. Model selection uncertainty arises when the data are used for both model selection and parameter estimation. Bias in estimators of model parameters often arise when data based selection has been done. Therefore, model averaging of the parameter estimators will be done to alleviate the bias in model selection in a set of candidate models, by combining the information from a set of candidate models. This paper is two-fold, new criteria of model selection are proposed based on different averages of AIC, BIC, AICc, and HQC. Also, model averaging is introduced to compare the parameter estimators in model averaging with the ones in model selection. Two Simulation studies are considered, the first is for model selection and showed that the new proposed criteria are lies between some of the known criteria such as AIC, BIC, AICc, and HQC, and so they can be used as new criteria of model selection. The second simulation study is for model averaging and showed that the parameter estimators have less bias and less predicted mean square error (PMSE) compared with the parameter estimators in model selection.

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Generalizing the derivation of the schwarz information criterion

Cited by 102 publications

References 37 publications

On hydrological model complexity, its geometrical interpretations and prediction uncertainty

On hydrological model complexity, its geometrical interpretations and prediction uncertainty

Characterizing regional groundwater flow in the Ethiopian Rift: A multimodel approach applied to Gidabo River Basin

New Criteria of Model Selection and Model Averaging in Linear Regression Models

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