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Results for “Uncertainty modelling”

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At least 109 records · Page 6Linked to original sources

PubMed2001

Congener-specific model for polychlorinated biphenyl effects on otter (Lutra lutra) and associated sediment quality criteria.

A model for risk assessment was built for simultaneous, congener-specific PCB bioaccumulation from sediment to fish to otters (Lutra lutra). Toxic equivalence factors (TEFs) were used to sum individual congeners in otters to a toxic equivalent concentration (TEQ) relative to 2,3,7,8-tetrachlorodibenzo-p-dioxin. Microbial dechlorination and burial in sediments and bioaccumulation are modeled to predict time trends of PCB concentrations in otters. Effects of accumulated PCBs on otters were assessed for vitamin A metabolism and reproduction, taking model uncertainty into account. Three locations in The Netherlands were modeled with PCB levels in sediment of 1 to 171 pg TEQ/g organic carbon (OC). Almost 100% reduction in litter size was predicted for the most polluted area in 1996. Due to large associated uncertainty, a period of 25 to 80 years may be needed for recovery of otter vitamin A levels and litter size at this site. Calculated median sediment quality criteria (SQC) range between 1 and 12 pg TEQ/g OC, depending on the chosen effect criterion. Uncertainty in calculated effects and SQCs is substantial and is mainly caused by uncertainty in PCB congener 126 accumulation.

Animals↗

PubMed2005

On the concept of model structural error.

A consideration of model structural error leads to some particularly interesting tensions in the model calibration/conditioning process. In applying models we can usually only assess the total error on some output variable for which we have observations. This total error may arise due to input and boundary condition errors, model structural errors and error on the output observation itself (not only measurement error but also as a result of differences in meaning between what is modelled and what is measured). Statistical approaches to model uncertainty generally assume that the errors can be treated as an additive term on the (possibly transformed) model output. This allows for compensation of all the sources of error, as if the model predictions are correct and the total error can be treated as "measurement error." Model structural error is not easily evaluated within this framework. An alternative approach to put more emphasis on model evaluation and rejection is suggested. It is recognised that model success or failure within this framework will depend heavily on an assessment of both input data errors (the "perfect" model will not produce acceptable results if driven with poor input data) and effective observation error (including a consideration of the meaning of observed variables relative to those predicted by a model).

Environment↗

PubMedDate not supplied

Uncertainty assessment of the model RICEWQ in northern Italy.

Model predictions are often seriously affected by uncertainties arising from many sources. Ignoring the uncertainty associated with model predictions may result in misleading interpretations when the model is used by a decision-maker for risk assessment. In this paper, an analysis of uncertainty was performed to estimate the uncertainty of model predictions and to screen out crucial variables using a Monte Carlo stochastic approach and a number of statistical methods, including ANOVA and stepwise multiple regression. The model studied was RICEWQ (Version 1.6.1), which was used to forecast pesticide fate in paddy fields. The results demonstrated that the paddy runoff concentration predicted by RICEWQ was in agreement with field measurements and the model can be applied to simulate pesticide fate at field scale. Model uncertainty was acceptable, runoff predictions conformed to a log-normal distribution with a short right tail, and predictions were reliable at field scale due to the narrow spread of uncertainty distribution. The main contribution of input variables to model uncertainty resulted from spatial (sediment-water partition coefficient and mixing depth to allow direct partitioning to bed) and management (time and rate of application) parameters, and weather conditions. Therefore, these crucial parameters should be carefully parameterized or precisely determined in each site-specific paddy field before the application of the model, since small errors of these parameters may induce large uncertainty of model outputs.

Forecasting↗

PubMed2000

Uncertainty in compartmental models for hazardous materials - a case study.

Performing uncertainty analysis on compartmental models is the main topic of this article. Elements of the methodology developed during a joint CEC/USNRC accident consequence code uncertainty analysis are introduced. The uncertainty is quantified using structured expert judgment. Experts are queried about physically observable quantities. Many code input parameters of the accident consequence codes are not physically observable but are used to predict observable quantities. Therefore, a probabilistic inversion technique was developed which 'transfers' the uncertainty from the physically observable quantities to the code input parameters. The probabilistic inversion technique is illustrated using the compartmental model of systemic retention of Sr in the human body. The article is concluded with a discussion on capturing uncertainty via compartmental models.

Hazardous Substances↗

PubMedDate not supplied

Complexity.

It is difficult to define complexity in modeling. Complexity is often associated with uncertainty since modeling uncertainty is an intrinsically difficult task. However, modeling uncertainty does not require, necessarily, complex models, in the sense of a model requiring an unmanageable number of degrees of freedom to characterize the aquifer. The relationship between complexity, uncertainty, heterogeneity, and stochastic modeling is not simple. Aquifer models should be able to quantify the uncertainty of their predictions, which can be done using stochastic models that produce heterogeneous realizations of aquifer parameters. This is the type of complexity addressed in this article.

Models, Theoretical↗

PubMed1996

A probabilistic model for deriving soil quality criteria based on secondary poisoning of top predators. I. Model description and uncertainty analysis.

In previous studies, the risk of toxicant accumulation in food chains was used to calculate quality criteria for surface water and soil. A simple algorithm was used to calculate maximum permissable concentrations [MPC = no-observed-effect concentration/bioconcentration factor(NOEC/BCF)]. These studies were limited to simple food chains. This study presents a method to calculate MPCs for more complex food webs of predators. The previous method is expanded. First, toxicity data (NOECs) for several compounds were corrected for differences between laboratory animals and animals in the wild. Second, for each compound, it was assumed these NOECs were a sample of a log-logistic distribution of mammalian and avian NOECs. Third, bioaccumulation factors (BAFs) for major food items of predators were collected and were assumed to derive from different log-logistic distributions of BAFs. Fourth, MPCs for each compound were calculated using Monte Carlo sampling from NOEC and BAF distributions. An uncertainty analysis for cadmium was performed to identify the most uncertain parameters of the model. Model analysis indicated that most of the prediction uncertainty of the model can be ascribed to uncertainty of species sensitivity as expressed by NOECs. A very small proportion of model uncertainty is contributed by BAFs from food webs. Correction factors for the conversion of NOECs from laboratory conditions to the field have some influence on the final value of MPC5, but the total prediction uncertainty of the MPC is quite large. It is concluded that the uncertainty in species sensitivity is quite large. To avoid unethical toxicity testing with mammalian or avian predators, it cannot be avoided to use this uncertainty in the method proposed to calculate MPC distributions. The fifth percentile of the MPC is suggested as a safe value for top predators.

Algorithms↗

PubMedDate not supplied

Innovations in bayes and empirical bayes methods: estimating parameters, populations and ranks.

By formalizing the relation among components and 'borrowing information' among them, Bayes and empirical Bayes methods can produce more valid, efficient and informative statistical evaluations than those based on traditional methods. In addition, Bayesian structuring of complicated models and goals guides development of appropriate statistical approaches and generates summaries which properly account for sampling and modelling uncertainty. Computing innovations enable implementation of complex and relevant models, thereby substantially increasing the role of Bayes/empirical Bayes methods in important statistical assessments. Policy-relevant statistical assessments involve synthesis of information from a set of related components such as medical clinics, geographic regions or research studies. Typical assessments include inference for individual parameters, synthesis over the collection of components (for example, the parameter histogram) and comparisons among parameters (for example, ranks). The relative importance of these goals depends on the context. Bayesian structuring provides a guide to valid inference. For example, while posterior means are the 'obvious' and optimal estimates for individual components under squared error loss, their empirical distribution function (EDF) is underdispersed and never valid for estimating the EDF of the true, underlying parameters. Effective histogram estimates result from optimizing a loss function based in a distance between the histogram and its estimate. Similarly, ranking observed data usually produces poor estimates and ranking posterior means can be inappropriate. Effective estimates should be based on a loss function that caters directly to ranks. Using examples of 'borrowing information', shrinkage and the variance/bias trade-off we motivate Bayes and empirical Bayes analysis. Then, we outline the formal approach and discuss 'triple-goal' estimates with values that when ranked produce optimal ranks, for which the EDF is an optimal estimate of the parameter EDF and such that the values themselves are effective estimates of co-ordinate-specific parameters. We use basic models and data analysis examples to highlight the conceptual and structural issues.

Animals↗

PubMedDate not supplied

Probabilistic analysis of decision trees using Monte Carlo simulation.

The authors describe methods for modeling uncertainty in the specification of decision tree probabilities and utilities using Monte Carlo simulation techniques. Exact confidence levels based upon the underlying probabilistic structure are provided. Probabilistic measures of sensitivity are derived in terms of classical information theory. These measures identify which variables are probabilistically important components of the decision. These techniques are illustrated in terms of the clinical problem of anticoagulation versus observation in the setting of deep vein thrombosis during the first trimester of pregnancy. These methods provide the decision analyst with powerful yet simple tools which give quantitative insight into the structure and inherent limitations of decision models arising from specification uncertainty. The techniques may be applied to complex decision models.

Adult↗

PubMed1996

A thermodynamic surface model for caesium sorption on bentonite.

Caesium sorption on Wyoming bentonite MX-80 has been studied in solutions of NaCl, KCl, MgCl(2), CaCl(2), NaNO(3) and Ca (NO(3))(2) of concentrations varying between 0.025 and 1 mol/L, as well as in a weakly saline (I=0.004 ml/L) and a strongly saline (I=0.46 mol/L) natural groundwater. These experiments have been used to derive a thermodynamic model for the interaction of caesium with the bentonite surface in accordance with a surface chemical model, including acid/base reactions developed recently for montmorillonite. The sorption behaviour of caesium on bentonite can be described, within the experimental and model uncertainties, in terms of a one-site ion exchange model. The ion exchange constant obtained for the reaction NaX+Cs(+) left arrow over right arrow CsX+Na(+) (where X represents the ion exchange sites on montmorillonite) is log(10) K(0)(ex)=1.6. Impurities in the bentonite, influencing the concentrations of competing cations, such as Na(+), K(+), Mg(2+) and Ca(2+), have a crucial impact on the sorption of caesium. This impact can be adequately quantified with the present model. The model predictions compare well with sorption data published in the open literature on both Wyoming bentonite MX-80 and other types of bentonite. Distribution coefficients from the literature obtained from both batch and diffusion experiments and varying over four orders of magnitude are reproduced and explained successfully by the model.

Journal Article↗

PubMed2005

Matrix models for childhood infections: a Bayesian approach with applications to rubella and mumps.

Mathematical modelling is an established tool for planning and monitoring vaccination programmes. However, the matrices describing contact rates are based on subjective choices, which have a large impact on results. This paper reviews published models and obtains prior model probabilities based on publication frequency and expert opinion. Using serological survey data on rubella and mumps, Bayesian methods of model choice are applied to select the most plausible models. Estimates of the basic reproduction number R0 are derived, taking into account model uncertainty and individual heterogeneity in contact rates. Twenty-two models are documented, for which publication frequency and expert opinion are negatively correlated. Using the expert prior with individual heterogeneity, R0=6.1 [95% credible region (CR) 4.3-9.2] for rubella and R0=19.3 (95% CR 4.0-31.5) for mumps. The posterior modes are insensitive to the prior for rubella but not for mumps. Overall, assortative models with individual heterogeneity are recommended.

Bayes Theorem↗

PubMed2005

Uncertainty and precaution in environmental management.

In this paper, two different visions of the relationship between science and policy are contrasted with one another: the "modern" vision and the "precautionary" vision. Conditions which must apply in order to invoke the Precautionary Principle are presented, as are some of the main challenges posed by the principle. The following central question remains: If scientific certainty cannot be provided, what may then justify regulatory interventions, and what degree of intervention is justifiable? The notion of "quality of information" is explored, and it is emphasized that there can be no absolute definition of good or bad quality. Collective judgments of quality are only possible through deliberation on the characteristics of the information, and on the relevance of the information to the policy context. Reference to a relative criterion therefore seems inevitable and legal complexities are to be expected. Uncertainty is presented as a multidimensional concept, reaching far beyond the conventional statistical interpretation of the concept. Of critical importance is the development of methods for assessing qualitative categories of uncertainty. Model quality assessment should observe the following rationale: identify a model that is suited to the purpose, yet bears some reasonable resemblance to the "real" phenomena. In this context, "purpose" relates to the policy and societal contexts in which the assessment results are to be used. It is therefore increasingly agreed that judgment of the quality of assessments necessarily involves the participation of non-modellers and non-scientists. A challenging final question is: How to use uncertainty information in policy contexts? More research is required in order to answer this question.

Decision Making↗

PubMedDate not supplied

Contaminant transport models under random sources.

While the discussion of model uncertainty has centered on spatial heterogeneity, it is possible that ground water models have not enjoyed much success as predictive tools often because the sources that were eventually imposed in the field differed from those represented in the simulations. This is because deterministic prediction of future conditions is often inaccurate due to the random nature of contaminant sources, in terms of their timing, location, and magnitude. This paper presents a stochastic framework for accommodating random contaminant sources in conventional, deterministic advection-dispersion transport models. The contaminant sources are first classified into two types: those occurring continuously with a deterministic component and random variations and those occurring randomly at instantaneous discrete-time intervals. For the first type, the governing partial differential equation (PDE) is replaced by a stochastic PDE. The random variations are modeled by Gaussian noise or Brownian motion, and the solution is obtained by using Ito's integration technique. For the second type, Markovian analysis is used for discrete-time contamination events. Both approaches use a deterministic transport model to generate response functions at any observation location and time. The response functions are then integrated to yield probabilistic description of contaminant transport, from which key statistical properties such as mean, standard deviation, and confidence interval can be drawn.

Forecasting↗

PubMed2006

Correlation between peak spatial-average SAR and temperature increase due to antennas attached to human trunk.

This paper discusses the correlation between peak spatial-average specific absorption rate (SAR) and maximum temperature increase for antennas attached to the human trunk. Frequency bands considered are 150, 400, and 900 MHz, which are assigned for occupational communications. This problem is throughly investigated with the aid of Green's function. In particular, the effect of variation of thermal constants on the temperature increase is revealed by using one-dimensional model. Computational results suggests that one of the most dominant factors which affect the correlation between peak SAR and maximum temperature increase is blood flow in tissues. This is confirmed by considering a three-dimensional realistic human body model. Uncertainties caused by the calculation of peak SAR and the difference in the body model shape are also quantified.

Back↗

PubMed1988

Effects of dosimetric and clinical uncertainty on complication-free local tumor control.

A mathematical description is developed to demonstrate the effects of uncertainty on complication-free local tumor control. Responses of tumors and normal tissues are modeled by conventional radiobiological models. Uncertainties are considered in the delivery of absorbed dose to the target volume and the normal tissue at risk for complications. The degree by which uncertainties compromise complication-free local control for target volumes with various tumor cell burdens is calculated.

Computer Simulation↗

PubMed2004

An operational assessment of the application of the relative reduction factors in the demonstration of attainment of the 8-hr ozone National Ambient Air Quality Standard.

The U.S. Environmental Protection Agency in 1997 revised the 1-hr ozone (O3) National Ambient Air Quality Standard (NAAQS) to one based on an 8-hr average, resulting in potential nonattainment status for substantial portions of the eastern United States. The regulatory process provides for the development of a state implementation plan that includes a demonstration that the projected future O3 concentrations will be at or below the NAAQS based on photochemical modeling and analytical techniques. In this study, four photochemical modeling systems, based on two photochemical models, Community Model for Air Quality and the Comprehensive Air Quality Model with extensions, and two emissions processing models, Sparse Matrix Optimization Kernel for Emissions and Emissions Modeling System, were applied to the eastern United States, with emphasis on the northeastern Ozone Transport Region in terms of their response to oxides of nitrogen and volatile organic carbon-focused controls on the estimated design values. With the 8-hr O3 NAAQS set as a bright-line test, it was found that a given area could be termed as being in or out of attainment of the NAAQS depending upon the modeling system. This suggests the need to provide an estimate of model-to-model uncertainty in the relative reduction factor (RRF) for a better understanding of the uncertainty in projecting the status of an area's attainment. Results indicate that the model-to-model differences considered in this study introduce

Air Pollutants↗

PubMed2005

Model of remote-sensing reflectance including bidirectional effects for case 1 and case 2 waters.

A remote-sensing reflectance model based on a lookup table is proposed for use in analyzing satellite ocean color data in both case 1 and case 2 waters. The model coefficients are tabulated for grid values of three angles--solar zenith, sensor zenith, and relative azimuth--to take account of directional variation. This model also requires, as input, a phase function parameter defined by the contribution of suspended particles to the backscattering coefficient. The model is generated from radiative transfer simulations for a wide range of inherent optical properties that cover both case 1 and 2 waters. The model uncertainty that is due to phase function variability is significantly reduced from that in conventional models. Bidirectional variation of reflectance is described and explained for a variety of cases. The effects of wind speed and cloud cover on bidirectional variation are also considered, including those for the fully overcast case in which angular variation can still be considerable (approximately 10%). The implications for seaborne validation of satellite-derived water-leaving reflectance are discussed.

Journal Article↗

PubMed2006

Markov Chain Monte Carlo Algorithm based metabolic flux distribution analysis on Corynebacterium glutamicum.

MOTIVATION: Metabolic flux analysis via a (13)C tracer experiment has been achieved using a Monte Carlo method with the assumption of system noise as Gaussian noise. However, an unbiased flux analysis requires the estimation of fluxes and metabolites jointly without the restriction on the assumption of Gaussian noise. The flux distributions under such a framework can be freely obtained with various system noise and uncertainty models. RESULTS: In this paper, a stochastic generative model of the metabolic system is developed. Following this, the Markov Chain Monte Carlo (MCMC) approach is applied to flux distribution analysis. The disturbances and uncertainties in the system are simplified as truncated Gaussian multiplicative models. The performance in a real metabolic system is illustrated by the application to the central metabolism of Corynebacterium glutamicum. The flux distributions are illustrated and analyzed in order to understand the underlying flux activities in the system. AVAILABILITY: Algorithms are available upon request.

Algorithms↗

PubMed2004

Bayesian model averaging in EEG/MEG imaging.

In this paper, the Bayesian Theory is used to formulate the Inverse Problem (IP) of the EEG/MEG. This formulation offers a comparison framework for the wide range of inverse methods available and allows us to address the problem of model uncertainty that arises when dealing with different solutions for a single data. In this case, each model is defined by the set of assumptions of the inverse method used, as well as by the functional dependence between the data and the Primary Current Density (PCD) inside the brain. The key point is that the Bayesian Theory not only provides for posterior estimates of the parameters of interest (the PCD) for a given model, but also gives the possibility of finding posterior expected utilities unconditional on the models assumed. In the present work, this is achieved by considering a third level of inference that has been systematically omitted by previous Bayesian formulations of the IP. This level is known as Bayesian model averaging (BMA). The new approach is illustrated in the case of considering different anatomical constraints for solving the IP of the EEG in the frequency domain. This methodology allows us to address two of the main problems that affect linear inverse solutions (LIS): (a) the existence of ghost sources and (b) the tendency to underestimate deep activity. Both simulated and real experimental data are used to demonstrate the capabilities of the BMA approach, and some of the results are compared with the solutions obtained using the popular low-resolution electromagnetic tomography (LORETA) and its anatomically constraint version (cLORETA).

Artifacts↗