Forecasting Acidification Effects Using a Bayesian Calibration and Uncertainty Propagation Approach

X-ray fluorescence (XRF) calibration for quantitative analysis is typically performed using certified reference materials (CRMs), where the relationship between the concentration of an element and the net area of its peak in the spectrum is assumed, after properly applying corrections for possible matrix effects, to be linear. The calibration is often obtained by Ordinary Least Squares (OLS) by minimizing the vertical distance between regression line and data points taking into account the experimental uncertainty. However, uncertainties in CRM-certified concentrations are often neglected, potentially leading to underestimated errors in the calibration model. In this work, a Bayesian approach is employed to obtain calibration curves by minimizing the orthogonal distance, taking into account both experimental and certified uncertainties. Twenty-four geological, soil, and sediment CRMs were analyzed using an energy-dispersive XRF spectrometer, and the resulting spectra were employed for constructed calibration curves for eight oxides and seven elements. The model parameters were estimated via maximum a posteriori (MAP) optimization and the posterior was evaluated by a Gibbs sampling algorithm in an orthogonal parameter space. A principal components analysis (PCA) was implemented for this coordinate transformation to remove the linear correlation. Validation against independent samples shows that the Bayesian approach demonstrates that the ordinary least-squares regression calibration curve deviates from the orthogonal Bayesian MAP curve by up to one standard deviation, particularly for elements with higher reference material variability and lower concentrations. Mean absolute errors and root mean squared errors indicate improved predictive performance for major oxides, while trace elements exhibit variable agreement due to instrumental and sample-specific factors. The results demonstrate that orthogonal Bayesian XRF calibration can enhance both accuracy and uncertainty quantification in multi-elemental analyses. • Novel Bayesian calibration for XRF accounts for uncertainties in both net peak area and CRM-certified concentrations. • Significant discrepancies between Bayesian and OLS regressions are observed where CRM uncertainties are high. • MCMC sampling provides full posterior distributions for parameters, enabling credible intervals and LOD estimates.

Simulation models inform health policy decisions by integrating data from multiple sources and forecasting outcomes when there is a lack of comprehensive evidence from empirical studies. Such models have long supported health policy for cancer, the first or second leading cause of death in over 100 countries. Discrete-event simulation (DES) and Bayesian calibration have gained traction in the field of Decision Science because they enable efficient and flexible modeling of complex health conditions and produce estimates of model parameters that reflect real-world disease epidemiology and data uncertainty given model constraints. This uncertainty is then propagated to model-generated outputs, enabling decision makers to determine the optimal strategy to recommend, assess confidence in the recommendation, and estimate the value of collecting additional information. However, there is limited end-to-end guidance on structuring a DES model for cancer progression, estimating its parameters using Bayesian calibration, and applying the calibration outputs to policy evaluation and other downstream tasks. To fill this gap, we introduce the DES Model for Cancer Interventions and Population Health in R (DESCIPHR), an open-source framework and codebase integrating a flexible DES model for the natural history of cancer, Bayesian calibration for parameter estimation, and screening strategy evaluation. We also introduce an automated method to generate data-informed parameter prior distributions and enhance the accuracy and flexibility of a neural network emulator-based Bayesian calibration algorithm. We anticipate that the adaptable DESCIPHR modeling template will facilitate the construction of future decision models evaluating the risks and benefits of health interventions.

Prioritization of sediment management alternatives using stochastic multicriteria acceptability analysis

Applied ecology has traditionally approached management problems through a simplified, single-species lens. Repeated failures of single-species management have led us to a new paradigm - managing at the ecosystem level. Ecosystem management involves a complex array of interacting organisms, processes and scientific disciplines. Accounting for interactions, feedback loops and dependencies between ecosystem components is therefore fundamental to understanding and managing ecosystems. We provide an overview of the main types of ecosystem models and their uses, and discuss challenges related to modelling complex ecological systems. Existing modelling approaches typically attempt to do one or more of the following: describe and disentangle ecosystem components and interactions; make predictions about future ecosystem states; and inform decision making by comparing alternative strategies and identifying important uncertainties. Modelling ecosystems is challenging, particularly when balancing the desire to represent many components of an ecosystem with the limitations of available data and the modelling objective. Explicitly considering different forms of uncertainty is therefore a primary concern. We provide some recommended strategies (such as ensemble ecosystem models and multi-model approaches) to aid the explicit consideration of uncertainty while also meeting the challenges of modelling ecosystems.

Identifying appropriate strategies for sustainable harvest is a challenge for many terrestrial vertebrate species because of uncertain system dynamics, limited data to inform population models, and potentially conflicting objectives that seek to harvest and maintain populations at desirable levels. The absence of monitoring and assessment infrastructure needed to regularly estimate abundance accentuates this challenge for many species, and limits application of rigorous state-dependent frameworks for decision making that are commonly advocated in natural resource management. Reference points, which define management targets or triggers for changing management, are often used to guide decision-making, but suffer from ambiguity when developed without explicit consideration of uncertainty or trade-offs among competing objectives. We describe an approach for developing unambiguous target reference points for assessment-limited species using structured decision making, and demonstrate the approach to develop target harvest rates for management of fall Wild Turkey (Meleagris gallopavo) harvests in the face of uncertain population and harvest dynamics. We use simulation and decision analyses to identify harvest rates that are optimal for accomplishing explicit management objectives in the face of uncertainty, and harvest rates with robust performance over broad regions of the demographic and harvest model parameter space. We demonstrate that population and harvest parameters commonly uncertain to wildlife managers interact to determine appropriate target harvest rates for Wild Turkeys, and that formally acknowledging a range of plausible values for structurally uncertain parameters results in more conservative target reference points than suggested by previously published studies. The structured decision making framework described here provides a natural conceptual and quantitative framework for extending our approach to develop unambiguous harvest targets for other assessment-limited wildlife populations while formally acknowledging structural uncertainty in system dynamics.

Uncertainty in pest control thresholds: Application to chemical control of corn earworm on soybean

Random fatigue of plane frames via lumped damage mechanics

This paper reviews the principles of scenario-based planning and illustrates an application of this approach in a study of a regional water supply and demand in northeastern Illinois. The scenario-based planning has been adopted over the traditional approaches because the scenario approach facilitates an explicit consideration of uncertainty in both supply and demand. An important component of the study was the development of scenario-based forecasts of water demand for major user sectors and geographical subareas within the 11-county region which, includes the city of Chicago and 250 municipalities. The study revealed that the increase in total withdrawals in 2050, under baseline scenario, would be 530 mgd (millions of gallons per day) (36 %) and could reach as high as 949 mgd (64 %) under high demand growth scenario. Thus, meeting these additional demands would require large capital outlays for water infrastructure and would likely have significant impacts on some of the regional sources of water supply...

Microwave links for rainfall estimation in an urban environment: Insights from an experimental setup in Luxembourg-City

The ability to accurately predict patterns of species' occurrences is fundamental to the successful management of animal communities. To determine optimal management strategies, it is essential to understand species-habitat relationships and how species habitat use is related to natural or human-induced environmental changes. Using five years of monitoring data in the Chesapeake and Ohio Canal National Historical Park, Maryland, USA, we developed four multispecies hierarchical models for estimating amphibian wetland use that account for imperfect detection during sampling. The models were designed to determine which factors (wetland habitat characteristics, annual trend effects, spring/summer precipitation, and previous wetland occupancy) were most important for predicting future habitat use. We used the models to make predictions about species occurrences in sampled and unsampled wetlands and evaluated model projections using additional data. Using a Bayesian approach, we calculated a posterior distribution of receiver operating characteristic area under the curve (ROC AUC) values, which allowed us to explicitly quantify the uncertainty in the quality of our predictions and to account for false negatives in the evaluation data set. We found that wetland hydroperiod (the length of time that a wetland holds water), as well as the occurrence state in the prior year, were generally the most important factors in determining occupancy. The model with habitat-only covariates predicted species occurrences well; however, knowledge of wetland use in the previous year significantly improved predictive ability at the community level and for two of 12 species/species complexes. Our results demonstrate the utility of multispecies models for understanding which factors affect species habitat use of an entire community (of species) and provide an improved methodology using AUC that is helpful for quantifying the uncertainty in model predictions while explicitly accounting for detection biases.

Abstract. Sensitivity analysis of atmospheric models is necessary to identify the processes that lead to uncertainty in model predictions, to help understand model diversity through comparison of driving processes, and to prioritise research. Assessing the effect of parameter uncertainty in complex models is challenging and often limited by CPU constraints. Here we present a cost-effective application of variance-based sensitivity analysis to quantify the sensitivity of a 3-D global aerosol model to uncertain parameters. A Gaussian process emulator is used to estimate the model output across multi-dimensional parameter space, using information from a small number of model runs at points chosen using a Latin hypercube space-filling design. Gaussian process emulation is a Bayesian approach that uses information from the model runs along with some prior assumptions about the model behaviour to predict model output everywhere in the uncertainty space. We use the Gaussian process emulator to calculate the percentage of expected output variance explained by uncertainty in global aerosol model parameters and their interactions. To demonstrate the technique, we show examples of cloud condensation nuclei (CCN) sensitivity to 8 model parameters in polluted and remote marine environments as a function of altitude. In the polluted environment 95 % of the variance of CCN concentration is described by uncertainty in the 8 parameters (excluding their interaction effects) and is dominated by the uncertainty in the sulphur emissions, which explains 80 % of the variance. However, in the remote region parameter interaction effects become important, accounting for up to 40 % of the total variance. Some parameters are shown to have a negligible individual effect but a substantial interaction effect. Such sensitivities would not be detected in the commonly used single parameter perturbation experiments, which would therefore underpredict total uncertainty. Gaussian process emulation is shown to be an efficient and useful technique for quantifying parameter sensitivity in complex global atmospheric models.

Bayesian parameter and joint probability distribution estimation for a hysteretic constitutive model of reinforcing steel

Bayesian neural networks for flight trajectory prediction and safety assessment

A Bayesian hierarchical framework for calibrating aquatic biogeochemical models

Calibration is a costly, necessary part of sensor manufacturing. Bayesian sensor calibration leverages prior knowledge in the form of a sample of sensor response functions from a sensor ensemble such as a fabrication lot. Based on a response model with <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">M</i> parameters, it allows to infer the measurand of interest and its predictive uncertainty from output signals of specimens of the ensemble after their lean calibration with a small number <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N</i> of measurements, possibly with <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${N}\lt {M}$ </tex-math></inline-formula>. This article answers the question of whether it is possible to reduce model complexity by choosing models with parameter number <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\widetilde {\textit {M}}\lt {M}$ </tex-math></inline-formula>, while guaranteeing a required predictive accuracy. Reduced models are obtained by projections of a high-dimensional model, termed full model, onto a subspace of its parameter space. An I-optimality-based loss function implementing the Bayesian calibration approach is derived. For given <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N</i> and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\widetilde {\textit {M}}$ </tex-math></inline-formula>, it allows to find an optimal reduced model and, at the same time, the optimal experimental design of the calibration. The approach is applied to 48 specimens of a CMOS Hall sensor system cross-sensitive to temperature and mechanical stress. Starting from an 11-parameter full model, reduced models with <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\widetilde {\textit {M}}={2},{4}$ </tex-math></inline-formula>, and 5 are identified for calibration routines with <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${N}={2},{4}$ </tex-math></inline-formula>, and 6 measurements, respectively. Despite the significantly smaller parameter numbers, the resulting root mean square (rms) predictive uncertainties of 102, 77.0, and 64.8 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\mu $ </tex-math></inline-formula>T, respectively, are increased by less than <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${1}\%$ </tex-math></inline-formula> from the full-model values. A general conclusion is that model order reduction (MOR) in the present Bayesian framework invariably entails an uncertainty increase, similar to principal component analysis (PCA).