Bayesian inference and predictive performance of soil respiration models in the presence of model discrepancy

Elshall, Ahmed S.; Ye, Ming; Niu, Guo Yue; Barron‐Gafford, Greg A.

doi:10.5194/gmd-12-2009-2019

Cited by 7 publications

(3 citation statements)

References 102 publications

(170 reference statements)

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“…They further suggest that inclusion of ‘process variation’, and not excessive down‐weighing of data, is more likely to provide robust estimation. In Bayesian inference of soil respiration models, Elshall et al (2019) suggest that there is often an assumption of independent, normally distributed and homoscedastic residuals. Furthermore, they suggest not accounting for these may not result in biased predictions and parameter estimates however, it will lead to underestimated posterior uncertainties and poorer predictions.…”

Section: Discussionmentioning

confidence: 99%

Issues in calibrating models with multiple unbalanced constraints: the significance of systematic model and data errors

et al. 2022

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Calibrating process‐based models using multiple constraints often improves the identifiability of model parameters, helps to avoid several errors compensating each other and produces model predictions that are more consistent with underlying processes. However, using multiple constraints can lead to predictions for some variables getting worse. This is particularly common when combining data sources with very different sample sizes. Such unbalanced model‐data fusion efforts are becoming increasingly common, for example when combining manual and automated measurements. Here we use a series of simulated virtual data experiments that aim to demonstrate and disentangle the underlying cause of issues that can occur when calibrating models with multiple unbalanced constraints in combination with systematic errors in models and data. We propose a diagnostic tool to help identify whether a calibration is failing due to these factors. We also test the utility of adding terms representing uncertainty in systematic model/data systematic error in calibrations. We show that unbalanced data by itself is not the problem—when fitting simulated data to the ‘true’ model, we can correctly recover model parameters and the true dynamics of latent variables. However, when there are systematic errors in the model or the data, we cannot recover the correct parameters. Consequently, the modelled dynamics of the low data volume variables departs significantly from the true values. We demonstrate the utility of the diagnostic tool and show that it can also be used to identify the extent of the imbalance before the calibration starts to ignore the more sparse data. Finally, we show that representing uncertainty in model structural errors and data biases in the calibration can greatly improve the model fit to low‐volume data, and improve coverage of uncertainty estimates. We conclude that the underlying issue is not one of sample size or information content per se, despite the popularity of ad hoc approaches that focus on ‘weighting’ datasets to achieve balance. Our results emphasize the importance of considering model structural deficiencies and data systematic biases in the calibration of process‐based models.

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Section: Discussionmentioning

confidence: 99%

Issues in calibrating models with multiple unbalanced constraints: the significance of systematic model and data errors

et al. 2022

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“…Rahmstorf et al [20] notes that residuals in global average temperature records are serially autocorrelated but ignored the autocorrelation and used a white-noise noise model, as inclusion of a more complex noise model would make the 'global warming hiatus' less statistically significant [20], and thus be counterproductive to showing that the 'global warming hiatus' did not reach any reasonable threshold of significance. Here however, we are examining the reverse question and hence ignoring the autocorrelation will create an underestimate in the amount of time needed to detect a change in warming trend, and underestimate uncertainty [28]. Thus we must include a more complex noise model for this study.…”

Section: Global Warming Slowdownmentioning

confidence: 99%

Detecting climate milestones on the path to climate stabilization

MacDougall,

Rogelj,

Jones

et al. 2024

Environ. Res. Lett.

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The era of anthropogenic climate change can be described by defined climate milestones. These milestones mark changes in the historic trajectory of change, and include peak greenhouse gas emissions, peak greenhouse gas concentration, deceleration of warming, net-zero emissions, and a transition to global cooling. However, given internal variability in the Earth system and measurement uncertainty, definitively saying that a milestone has passed requires rigour. Here CMIP6 simulations of peak-and-decline scenarios are used to examine the time needed to robustly detect three climate milestones: 1) the slowdown of global warming; 2) the end of global surface temperature increase; and 3) peak concentration of CO2. It is estimated that it will take 40 to 60 years after a simulated slowdown in warming rate, to robustly detect (>95% change) the signal in the global average temperature record. Detecting when warming has stopped will also be difficult and it takes until the mid 22nd century to have enough data to conclude warming has stopped. Detecting that CO2 concentration has peaked is far easier and a drop in CO2 concentration of 3 ppm is consistent with a greater than 99% chance that CO2 has peaked in all scenarios examined. Thus it is likely that as the rate of CO2 emissions is reduced, and net-zero emissions is approached, interpreting the global temperature record will become difficult -- with a high potential to create confusion amongst policy makers and the general public.

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“…Thus, the scope of this work is the accurate estimation of BME given different Monte Carlo estimators. Studying the impact of prior distribution [72], likelihood function [73,74] , model fidelity [12,14,15,47] , prior model probability [13], input data [75], and observation data [2,12] on the magnitude of BME is beyond the scope of this work. The readers are refered to a recent review article that discusses multi-model analysis in hydrology using Bayesian techiques [76].…”

Section: Introductionmentioning

confidence: 99%

Making Steppingstones out of Stumbling Blocks: A Bayesian Model Evidence Estimator with Application to Groundwater Transport Model Selection

Elshall

2019

Water

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Bayesian model evidence (BME) is a measure of the average fit of a model to observation data given all the parameter values that the model can assume. By accounting for the trade-off between goodness-of-fit and model complexity, BME is used for model selection and model averaging purposes. For strict Bayesian computation, the theoretically unbiased Monte Carlo based numerical estimators are preferred over semi-analytical solutions. This study examines five BME numerical estimators and asks how accurate estimation of the BME is important for penalizing model complexity. The limiting cases for numerical BME estimators are the prior sampling arithmetic mean estimator (AM) and the posterior sampling harmonic mean (HM) estimator, which are straightforward to implement, yet they result in underestimation and overestimation, respectively. We also consider the path sampling methods of thermodynamic integration (TI) and steppingstone sampling (SS) that sample multiple intermediate distributions that link the prior and the posterior. Although TI and SS are theoretically unbiased estimators, they could have a bias in practice arising from numerical implementation. For example, sampling errors of some intermediate distributions can introduce bias. We propose a variant of SS, namely the multiple one-steppingstone sampling (MOSS) that is less sensitive to sampling errors. We evaluate these five estimators using a groundwater transport model selection problem. SS and MOSS give the least biased BME estimation at an efficient computational cost. If the estimated BME has a bias that covariates with the true BME, this would not be a problem because we are interested in BME ratios and not their absolute values. On the contrary, the results show that BME estimation bias can be a function of model complexity. Thus, biased BME estimation results in inaccurate penalization of more complex models, which changes the model ranking. This was less observed with SS and MOSS as with the three other methods.

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Bayesian inference and predictive performance of soil respiration models in the presence of model discrepancy

Cited by 7 publications

References 102 publications

Issues in calibrating models with multiple unbalanced constraints: the significance of systematic model and data errors

Issues in calibrating models with multiple unbalanced constraints: the significance of systematic model and data errors

Detecting climate milestones on the path to climate stabilization

Making Steppingstones out of Stumbling Blocks: A Bayesian Model Evidence Estimator with Application to Groundwater Transport Model Selection

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