Uncertainty In Model Predictions Research Articles

An integrated quantitative systems pharmacology virtual population approach for calibration with oncology efficacy endpoints.

In drug development, quantitative systems pharmacology (QSP) models are becoming an increasingly important mathematical tool for understanding response variability and for generating predictions to inform development decisions. Virtual populations are essential for sampling uncertainty and potential variability in QSP model predictions, but many clinical efficacy endpoints can be difficult to capture with QSP models that typically rely on mechanistic biomarkers. In oncology, challenges are particularly significant when connecting tumor size with time-to-event endpoints like progression-free survival while also accounting for censoring due to consent withdrawal, loss in follow-up, or safety criteria. Here, we expand on our prior work and propose an extended virtual population selection algorithm that can jointly match tumor burden dynamics and progression-free survival times in the presence of censoring. We illustrate the core components of our algorithm through simulation and calibration of a signaling pathway model that was fitted to clinical data for a small molecule targeted inhibitor. This methodology provides an approach that can be tailored to other virtual population simulations aiming to match survival endpoints for solid-tumor clinical datasets.

Unraveling Uncertainty: The Impact of Biological and Analytical Variation on the Prediction Uncertainty of Categorical Prediction Models.

Interest in prediction models, including machine learning (ML) models, based on laboratory data has increased tremendously. Uncertainty in laboratory measurements and predictions based on such data are inherently intertwined. This study developed a framework for assessing the impact of biological and analytical variation on the prediction uncertainty of categorical prediction models. Practical application was demonstrated for the prediction of renal function loss (Chronic Kidney Disease Epidemiology Collaboration [CKD-EPI] equation) and 31-day mortality (advanced ML model) in 6360 emergency department patients. Model outcome was calculated in 100 000 simulations of variation in laboratory parameters. Subsequently, the percentage of discordant predictions was calculated with the original prediction as reference. Simulations were repeated assuming increasing levels of analytical variation. For the ML model, area under the receiver operating characteristic curve (AUROC), sensitivity, and specificity were 0.90, 0.44, and 0.96, respectively. At base analytical variation, the median [2.5th-97.5th percentiles] percentage of discordant predictions was 0% [0%-28.8%]. In addition, 7.2% of patients had >5% discordant predictions. At 6× base analytical variation, the median [2.5th-97.5th percentiles] percentage of discordant predictions was 0% [0%-38.8%]. In addition, 11.7% of patients had >5% discordant predictions. However, the impact of analytical variation was limited compared with biological variation. AUROC, sensitivity, and specificity were not affected by variation in laboratory parameters. The impact of biological and analytical variation on the prediction uncertainty of categorical prediction models, including ML models, can be estimated by the occurrence of discordant predictions in a simulation model. Nevertheless, discordant predictions at the individual level do not necessarily affect model performance at the population level.

Ensemble Learning for Stellar Classification and Radius Estimation from Multimodal Data

Abstract Stellar classification and radius estimation are crucial for understanding the structure of the universe and stellar evolution. With the advent of the era of astronomical big data, multimodal data are available and theoretically effective for stellar classification and radius estimation. A problem is how to improve the performance of this task by jointly using the multimodal data. However, existing research primarily focuses on using single-modal data. To this end, this paper proposes a model, Multi-Modal SCNet (MMSCNet), and its ensemble model Multimodal Ensemble for Stellar Classification and Regression (MESCR) for improving stellar classification and radius estimation performance by fusing two modality data. In this problem, a typical phenomenon is that the sample numbers of some type stars are evidently more than others. This imbalance has negative effects on model performance. Therefore, this work utilize a weighted sampling strategy to deal with the imbalance issues in MESCR. Some evaluation experiments are conducted on a test set for MESCR and the classification accuracy is 96.1\%, the radius estimation performance Mean of Absolute Error (MAE) and $\sigma$ are 0.084 dex and 0.149 \(R_{\odot}\) respectively. Moreover, we assessed the uncertainty of model predictions, confirming good consistency within a reasonable deviation range. Finally, we applied our model to 50,871,534 SDSS stars without spectra and published a new catalog.

Spectral expansion methods for prediction uncertainty quantification in systems biology

Uncertainty is ubiquitous in biological systems. For example, since gene expression is intrinsically governed by noise, nature shows a fascinating degree of variability. If we want to use a model to predict the behaviour of such an intrinsically stochastic system, we have to cope with the fact that the model parameters are never exactly known, but vary according to some distribution. A key question is then to determine how the uncertainties in the parameters affect the model outcome. Knowing the latter uncertainties is crucial when a model is used for, e.g., experimental design, optimisation, or decision-making. To establish how parameter and model prediction uncertainties are related, Monte Carlo approaches could be used. Then, the model is evaluated for a huge number of parameters sets, drawn from the multivariate parameter distribution. However, when model solutions are computationally expensive this approach is intractable. To overcome this problem, so-called spectral expansion (SE) methods have been developed to quantify prediction uncertainty within a probabilistic framework. Such SE methods have a basis in, e.g., computational mathematics, engineering, physics, and fluid dynamics, and, to a lesser extent, systems biology. The computational costs of SE schemes mainly stem from the calculation of the expansion coefficients. Furthermore, SE effectively leads to a surrogate model which captures the dependence of the model on the uncertainty parameters, but is much simpler to execute compared to the original model. In this paper, we present an innovative scheme for the calculation of the expansion coefficients. It guarantees that the model has to be evaluated only a restricted number of times. Especially for models of high complexity this may be a huge computational advantage. By applying the scheme to a variety of examples we show its power, especially in challenging situations where solutions slowly converge due to high computational costs, bifurcations, and discontinuities.

Vortex Trapping of Suspended Sand Grains Over Ripples

AbstractCoastal hydrodynamics and morphodynamics integrate the effects of small‐scale fluid‐sediment interactions; yet, these small‐scale processes are not well understood. To investigate sediment trapping by turbulent coherent structures or vortices, the transport of coarse sand over ripples was analyzed in a small‐oscillatory flow tunnel with phase‐separated Particle Image and Tracking Velocimetry. Results from one of the first direct measurements of vortex‐trapped sand grains under oscillatory flows are presented. The vortices mobilized sand grains along the ripple slopes just prior to flow reversal and transported the suspended sediment grains. During several flow cycles, some sand grains were temporarily trapped in the vortex, prescribing semi‐circular trajectories off‐center from the vortex core in quadrants of the vortex that were closest to the ripple slope, as illustrated by Nielsen (1992, https://doi.org/10.1142/1269). Comparisons of the horizontal sediment grain velocity with the horizontal fluid velocity yielded a linear relationship with a slope of 0.87. The vertical grain velocities also varied linearly with the vertical fluid velocity with a slope of approximately 1 and an offset of −0.08 m . The offset is close to the still water settling velocity for coarse sand grains, as hypothesized during vortex trapping. Additionally, estimates of the off‐center distance, between the centers of the semi‐circular sediment paths and vortex cores, compared well with the ratio of the settling velocity to the radian frequency of the vortex yielding a linear regression slope of 0.99. Improved understanding of vortex trapping effects on sediment dynamics may decrease uncertainty in model predictions of large‐scale coastal hydrodynamics and sediment transport.

Solar Insolation Prediction Based on Machine Learning: Error Analysis on Data Similarity and Predictive Model Uncertainty

Solar Insolation Prediction Based on Machine Learning: Error Analysis on Data Similarity and Predictive Model Uncertainty

Quantitative modeling and uncertainty estimation for small-sample LIBS using Gaussian negative log-likelihood and monte carlo dropout methods

Laser-induced breakdown spectroscopy (LIBS) has emerged as a powerful analytical technique widely applied in materials science, environmental monitoring, and other fields. In traditional quantitative analysis, models are established for the sample-to-element content based on acquired characteristic spectra combined with specific modeling methods. Small-sample LIBS poses significant challenges to researchers due to its high dimensionality and limited sample size, making it difficult for traditional modeling methods to establish effectively generalized and robust models. Addressing the issues of overfitting during training and the uncertainty of LIBS data, we developed an artificial neural network (ANN) model. Unlike traditional ANN which uses mean squared error functions as training losses, Gaussian negative log-likelihood (GLL) functions were used to train the model. This approach allows for simultaneous consideration of the quantitative prediction of sample element concentrations and the uncertainty of the quantification model prediction. Moreover, the Monte Carlo Dropout (MCDropout) method was applied to reduce prediction bias, resulting in a more robust, generalizable, and uncertainty-aware quantitative model. Compared to traditional quantitative methods, the method proposed in this paper achieved quantitative accuracies of 0.9877, 0.9939, 0.9876, and 0.9899 for four elements (Mn, Mo, Cr, Cu) in stainless steel, respectively. The uncertainty output effectively informs data comprehension and spectral analysis. To the best of our knowledge, this study is the first to propose utilizing model-quantified spectral uncertainty in LIBS quantitative tasks. This innovative study not only provides solutions for small-sample LIBS learning but also enhances the stability and accuracy of quantitative modeling by addressing the impact of uncertainty on training and reducing uncertainty. It is crucial for overcoming the limitations of traditional methods in small-sample LIBS quantification and achieving reliable real-time, high-precision LIBS detection, taking LIBS technology a step further towards practical reliability and precision.

Quantifying spatially explicit uncertainty in empirically downscaled climate data

AbstractEcological simulations including forest and vegetation growth models require climate inputs that match the resolution and extent of the process being modelled. Climate inputs are often derived at resolutions coarser than the scale of many ecosystem processes. Machine learning models can be trained to spatially downscale climate data to fine (30 m) resolution using topographic variables such as elevation, aspect and other site‐specific factors. Statistically downscaled climate models will have spatially varying uncertainty that is not usually incorporated into downscaling techniques for error propagation into later models, are often applied on smaller areas, are not fine enough resolutions for many modelling techniques, or are not always scalable to large spatial extents. There remains opportunity to leverage machine learning advancements to downscale climate to very fine (30 m) resolutions with associated spatially explicit uncertainty to represent microclimatic variation in ecological models. In this study, we used quantile machine learning to produce 30 m downscaled temperature and precipitation data and associated model prediction uncertainty for the state of California. Temperature models were accurate at downscaling 4 km climate data to 30 m, performing better than the 4 km data at high and low slope positions and at high elevations, especially where there were fewer weather observations. Precipitation model predictions did not show global improvement over the 4 km scale, but were more accurate at high elevations, slopes with higher solar radiation and in valleys. For all climate variables, the added detail of spatial explicit uncertainty via 90% prediction intervals provides critical insight into the utility of empirically downscaled climate. The resulting 30 m spatially contiguous outputs can be used as ecological model inputs with uncertainty propagation, to illuminate climate trends over time as a function of fine‐scale spatial factors, and to highlight areas of spatially explicit uncertainty.

Predicting rice phenology across China by integrating crop phenology model and machine learning

This study explores the integration of crop phenology models and machine learning approaches for predicting rice phenology across China, to gain a deeper understanding of rice phenology prediction. Multiple approaches were used to predict heading and maturity dates at 337 locations across the main rice growing regions of China from 1981 to 2020, including crop phenology model, machine learning and hybrid model that integrate both approaches. Furthermore, an interpretable machine learning (IML) using SHapley Additive exPlanation (SHAP) was employed to elucidate influence of climatic and varietal factors on uncertainty in crop phenology model predictions. Overall, the hybrid model demonstrated a high accuracy in predicting rice phenology, followed by machine learning and crop phenology models. The best hybrid model, based on a serial structure and the eXtreme Gradient Boosting (XGBoost) algorithm, achieved a root mean square error (RMSE) of 4.65 and 5.72 days and coefficient of determination (R2) values of 0.93 and 0.9 for heading and maturity predictions, respectively. SHAP analysis revealed temperature to be the most influential climate variable affecting phenology predictions, particularly under extreme temperature conditions, while rainfall and solar radiation were found to be less influential. The analysis also highlighted the variable importance of climate across different phenological stages, rice cultivation patterns, and geographic regions, underscoring the notable regionality. The study proposed that a hybrid model using an IML approach would not only improve the accuracy of prediction but also offer a robust framework for leveraging data-driven in crop modeling, providing a valuable tool for refining and advancing the modeling process in rice.

The impact of design and operational parameters on the optimal performance of direct air capture units using solid sorbents

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Structured methods for parameter inference and uncertainty quantification for mechanistic models in the life sciences.

Parameter inference and uncertainty quantification are important steps when relating mathematical models to real-world observations and when estimating uncertainty in model predictions. However, methods for doing this can be computationally expensive, particularly when the number of unknown model parameters is large. The aim of this study is to develop and test an efficient profile likelihood-based method, which takes advantage of the structure of the mathematical model being used. We do this by identifying specific parameters that affect model output in a known way, such as a linear scaling. We illustrate the method by applying it to three toy models from different areas of the life sciences: (i) a predator-prey model from ecology; (ii) a compartment-based epidemic model from health sciences; and (iii) an advection-diffusion reaction model describing the transport of dissolved solutes from environmental science. We show that the new method produces results of comparable accuracy to existing profile likelihood methods but with substantially fewer evaluations of the forward model. We conclude that our method could provide a much more efficient approach to parameter inference for models where a structured approach is feasible. Computer code to apply the new method to user-supplied models and data is provided via a publicly accessible repository.

Partitioning Uncertainty in Model Predictions from Compartmental Modeling of Global Carbon Cycle

Our comprehension of the real world remains perpetually incomplete, compelling us to rely on models to decipher intricate real-world phenomena. However, these models, at their pinnacle, serve merely as close approximations of the systems they seek to emulate, inherently laden with uncertainty. Therefore, investigating the disparities between observed system behaviors and model-derived predictions is of paramount importance. Although achieving absolute quantification of uncertainty in the model-building process remains challenging, there are avenues for both mitigating and highlighting areas of uncertainty. Central to this study are three key sources of uncertainty, each exerting significant influence: (i) structural uncertainty arising from inadequacies in mathematical formulations within the conceptual models; (ii) scenario uncertainty stemming from our limited foresight or inability to forecast future conditions; and (iii) input factor uncertainty resulting from vaguely defined or estimated input factors. Through uncertainty analysis, this research endeavors to understand these uncertainty domains within compartmental models, which are instrumental in depicting the complexities of the global carbon cycle. The results indicate that parameter uncertainty has the most significant impact on model outputs, followed by structural and scenario uncertainties. Evident deviations between the observed atmospheric CO2 content and simulated data underscore the substantial contribution of certain uncertainties to the overall estimated uncertainty. The conclusions emphasize the need for comprehensive uncertainty quantification to enhance model reliability and the importance of addressing these uncertainties to improve predictions related to global carbon dynamics and inform policy decisions. This paper employs partitioning techniques to discern the contributions of the aforementioned primary sources of uncertainty to the overarching prediction uncertainty.

Drug safety assessment by machine learning models

ABSTRACT The evaluation of drug-induced Torsades de pointes (TdP) risks is crucial in drug safety assessment. In this study, we discuss machine learning approaches in the prediction of drug-induced TdP risks using preclinical data. Specifically, a random forest model was trained on the dataset generated by the rabbit ventricular wedge assay. The model prediction performance was measured on 28 drugs from the Comprehensive In Vitro Proarrhythmia Assay initiative. Leave-one-drug-out cross-validation provided an unbiased estimation of model performance. Stratified bootstrap revealed the uncertainty in the asymptotic model prediction. Our study validated the utility of machine learning approaches in predicting drug-induced TdP risks from preclinical data. Our methods can be extended to other preclinical protocols and serve as a supplementary evaluation in drug safety assessment.

Does high-latitude ionospheric electrodynamics exhibit hemispheric mirror symmetry?

Abstract. Ionospheric electrodynamics is a problem of mechanical stress balance mediated by electromagnetic forces. Joule heating (the total rate of frictional heating of thermospheric gases and ionospheric plasma) and ionospheric Hall and Pedersen conductances comprise three of the most basic descriptors of this problem. More than half a century after identification of their central role in ionospheric electrodynamics, several important questions about these quantities, including the degree to which they exhibit hemispheric symmetry under reversal of the sign of dipole tilt and the sign of the y component of the interplanetary magnetic field (so-called “mirror symmetry”), remain unanswered. While global estimates of these key parameters can be obtained by combining existing empirical models, one often encounters some frustrating sources of uncertainty: the measurements from which such models are derived, usually magnetic field and electric field or ion drift measurements, are typically measured separately and do not necessarily align. The models to be combined moreover often use different input parameters, different assumptions about hemispheric symmetry, and/or different coordinate systems. We eliminate these sources of uncertainty in model predictions of electromagnetic work J⋅E (in general not equal to Joule heating ηJ2) and ionospheric conductances by combining two new empirical models of the high-latitude ionospheric electric potential and ionospheric currents that are derived in a mutually consistent fashion: these models do not assume any form of symmetry between the two hemispheres; are based on Apex magnetic coordinates (denoted Apex), spherical harmonics, and the same model input parameters; and are derived exclusively from convection and magnetic field measurements made by the Swarm and CHAMP satellites. The model source code is open source and publicly available. Comparison of high-latitude distributions of electromagnetic work in each hemisphere as functions of dipole tilt and interplanetary magnetic field clock angle indicates that the typical assumption of mirror symmetry is largely justified. Model predictions of ionospheric Hall and Pedersen conductances exhibit a degree of symmetry, but clearly asymmetric responses to dipole tilt and solar wind driving conditions are also identified. The distinction between electromagnetic work and Joule heating allows us to identify where and under what conditions the assumption that the neutral wind corotates with the Earth is not likely to be physically consistent with predicted Hall and Pedersen conductances.

Leveraging conformal prediction to annotate enzyme function space with limited false positives.

Machine learning (ML) is increasingly being used to guide biological discovery in biomedicine such as prioritizing promising small molecules in drug discovery. In those applications, ML models are used to predict the properties of biological systems, and researchers use these predictions to prioritize candidates as new biological hypotheses for downstream experimental validations. However, when applied to unseen situations, these models can be overconfident and produce a large number of false positives. One solution to address this issue is to quantify the model's prediction uncertainty and provide a set of hypotheses with a controlled false discovery rate (FDR) pre-specified by researchers. We propose CPEC, an ML framework for FDR-controlled biological discovery. We demonstrate its effectiveness using enzyme function annotation as a case study, simulating the discovery process of identifying the functions of less-characterized enzymes. CPEC integrates a deep learning model with a statistical tool known as conformal prediction, providing accurate and FDR-controlled function predictions for a given protein enzyme. Conformal prediction provides rigorous statistical guarantees to the predictive model and ensures that the expected FDR will not exceed a user-specified level with high probability. Evaluation experiments show that CPEC achieves reliable FDR control, better or comparable prediction performance at a lower FDR than existing methods, and accurate predictions for enzymes under-represented in the training data. We expect CPEC to be a useful tool for biological discovery applications where a high yield rate in validation experiments is desired but the experimental budget is limited.

Nonstationary frequency analysis of extreme precipitation: Embracing trends in observations

Knowledge of the recurrence intervals of precipitation extremes is vital for infrastructure design, risk assessment, and insurance planning. However, trends and shifts in rainfall patterns globally pose challenges to the application of extreme value analysis (EVA) which relies critically on the assumption of stationarity. In this paper, we explore: (1) the suitability of nonstationary (NS) models in the presence of statistically significant trends, and (2) their potential in modeling out-of-sample data to improve frequency analysis of extreme precipitation. We analyze the benefits of using a nonstationary Generalized Extreme Value (GEV) model for annual extreme precipitation records from Southern Brazil. The location of the GEV distribution is allowed to change with time. The unknown GEV model parameters are estimated using Bayesian techniques coupled with Markov chain Monte Carlo simulation. Next, we use GAME sampling to compute the evidence (and their ratios, the so-called Bayes factors) for stationary and nonstationary models of annual maximum precipitation. Our results show that the presence of a statistically significant trend in annual maximum precipitation alone does not justify the use of a NS model. The location parameter of the GEV distribution must also be well defined, otherwise, stationary models of annual maximum precipitation receive more support by the data. These findings reiterate the importance of accounting for GEV model parameters and predictive uncertainty in frequency analysis and hypothesis testing of annual maximum precipitation data records. Furthermore, a meaningful EVA demands detailed knowledge about the origin and persistence of observed changes.

The Lifetime Health and Economic Burden of Smokeless Tobacco use in Bangladesh, India, and Pakistan: Results From ASTRAMOD.

Under the current policy landscapes, the lifetime health and economic burden of smokeless tobacco (ST) products, consumed by over 297 million ST users in South Asia, is unknown. The aim of this study was to estimate the lifetime health effects and costs attributable to current and future ST use in Bangladesh, India, and Pakistan where the majority of ST users live. We developed a Markov-based state-transition model (ASTRAMOD) to predict the lifetime costs of treatment of four diseases (oral, pharyngeal, esophageal cancers, and stroke) and disability-adjusted life years (DALYs), attributable to the current and future use of ST under existing ST policy scenario. Country-specific Global Adult Tobacco Surveys, life tables, and meta-analyses of South Asian and South East Asian studies were used to populate the model. A probabilistic sensitivity analysis evaluated the uncertainty in model predictions. If there were no change in the current ST policies, the lifetime ST-attributable treatment costs would be over US$19 billion in India, over US$1.5 billion in Bangladesh, and over US$3 billion in Pakistan. For all countries, the attributable costs are higher for younger cohorts with costs declining with increasing age for those over 50. The model predicted that a typical 15-year-old male adoloscent would gain 0.07-0.18 life years, avert 0.07-0.19 DALYs, and generate a cost-savings of US$7-21 on healthcare spending if ST policies were changed to eliminate ST use. Policy interventions aimed at decreasing the uptake of ST and increasing quitting success have the potential to substantially decrease the economic and health burden of ST. This study provides the most comprehensive estimates of the lifetime health and economic burden of ST by 5-year age and sex cohorts. This is also the first study that highlights the scale of health and economic burden of ST in Bangladesh, India, and Pakistan if there were no changes in the current ST policies. Policymakers and practitioners can use the reported data to justify their decisions to improve current ST policies and practices in their country. Researchers can use the ASTRAMOD methodology to estimate the impact of future ST policy changes.

Sea trials vs prediction by numerical models—Uncertainties in the measurements and prediction of WASP performance

Accurately predicting the power saving from wind-assisted ship propulsion is one of the most discussed topics in alternative and complementary propulsion methods. Aero- and hydrodynamic interactions between the sails and the ship increase the difficulty of modelling the propulsion contribution theoretically, but the sensibility of sail performance on the wind conditions increases the demands on measurement accuracy if the performance is to be measured in sea trials. This paper analyses and compares the uncertainties of sea trial tests and model predictions by means of parameter variation and Monte Carlo simulations. The results show that sea trials have an uncertainty of 23 %, well above 100 % of the measured savings, if performed using normal onboard equipment. Model uncertainties were found to be between 6 % and 17 % of the predicted savings.

Probabilistic assessment of scalar transport under hydrodynamically unstable flows in heterogeneous porous media

Quantitative predictions of scalar transport in natural porous media is a nontrivial task given the presence of multi-scale spatial heterogeneity in the permeability field. Due to data scarcity, the structural map of the permeability field is subject to uncertainty and therefore, model predictions are uncertain. For such reasons, probabilistic models of flow and transport in natural porous media are required in risk assessment and to provide reliable decision making under uncertainty. Further complexities arise when the viscosity of the injected solute differs from that of the ambient fluid. Under the presence of viscosity contrast, hydrodynamic instabilities give rise to viscous fingering, which induces additional disorder in both velocity and solute concentration fields. This work examines the combined role of viscous fingering and permeability heterogeneity in the probabilistic description of transport predictions. In particular, we focus on metrics that are important for risk analysis, such as the solute plume’s early arrival times and the maximum concentration observed at a given location. We propose to use the Projection Pursuit Adaptation (PPA) method in the Polynomial Chaos Expansion (PCE) framework to quantify uncertainty in transport model predictions. The PPA method is a data-driven approach that optimally represents a given quantity of interest in a low-dimensional manifold. Unlike other dimension reduction techniques in uncertainty quantification, the PPA method utilizes non-linear information of the quantity of interest to identify the low-dimensional manifold, thereby increasing the likelihood of finding a more accurate lower-dimensional space. Moreover, the PPA model converges to the physical solution in a mean squared sense with respect to the polynomial order, enabling the construction of a converged model even with limited available data. Then, the PPA results are compared to Monte Carlo simulations using the same amount of data. This comparison illustrates that while Monte Carlo simulations are able to capture low-order statistics, they struggle to represent more detailed probability density functions. Our results show how the combined effect of permeability heterogeneity and viscosity contrast can enhance the mobility of the solute plume.

UPH Problem 20 – reducing uncertainty in model prediction: a model invalidation approach based on a Turing-like test

Abstract. This study proposes using a Turing-like test for model evaluations and invalidations based on evidence of epistemic uncertainties in event runoff coefficients. Applying the consequent “limits of acceptability” results in all the 100 000 model parameter sets being rejected. However, applying the limits, together with an allowance for timing errors, to time steps ranked by discharge, results in an ensemble of 2064 models that can be retained for predicting discharge peaks. These do not include any of the models with the highest (> 0.9) efficiencies. The analysis raises questions about the impact of epistemic errors on model simulations, and the need for both better observed data and better models.