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Results for “Uncertainty modelling”

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PubMed1997

Equivalent methods to analyse dynamic experiments in which the input function is noisy.

A comparison is made between two methods of parameter estimation for analysis of dynamic experiments in which the input function is noisy. Noise in the input function leads to uncertainties in the calculated model-predicted values, and therefore the covariance matrix of the residuals is a function of the model parameters. Statistical uncertainties in the model-predicted values significantly change the nature of the fitting process and the quality of the results. The initial method uses a weighted least-squares criterion where the weighting matrix is the inverse of the full covariance matrix of the residuals, incorporating both the noise in the output data and the noise in the input function. The methodology was applied to dynamic emission tomography studies of the heart, where the blood (input) and tissue (output) tracer concentrations at each time are derived from two regions of interest in the same tomographic section. The second method introduces additional parameters to describe the input function, and adds terms to the weighted sum of squares which comprise the criterion. Instead of only summing the weighted terms to account for differences between the model and the output function, there is a second set of terms to account for the differences between the model and the input function. The two methods have different theoretical bases and appear to optimize different criteria, but it is shown here that they are equivalent to one another. The criterion which they minimize is the same under certain matrix invertibility constraints, which must be satisfied to ensure the stability of either method.

Models, Theoretical↗

PubMed2005

Sampling uncertainties for the detection of chemical agents in complex food matrices.

Using uncertainty associated with detection of aflatoxin in shelled corn as a model, the uncertainty associated with detecting chemical agents intentionally added to food products was evaluated. Accuracy and precision are two types of uncertainties generally associated with sampling plans. Sources of variability that affect precision were the primary focus of this investigation. Test procedures used to detect chemical agents generally include sampling, sample preparation, and analytical steps. The uncertainty of each step contributes to the total uncertainty of the test procedure. Using variance as a statistical measure of uncertainty, the variance associated with each step of the test procedure used to detect aflatoxin in shelled corn was determined for both low and high levels of contamination. For example, when using a 1-kg sample, Romer mill, 50-g subsample, and high-performance liquid chromatography to test a lot of shelled corn contaminated with aflatoxin at 10 ng/g, the total variance associated with the test procedure was 149.2 (coefficient of variation of 122.1%). The sampling, sample preparation, and analytical steps accounted for 83.0, 15.6, and 1.4% of the total variance, respectively. A variance of 149.2 suggests that repeated test results will vary from 0 to 33.9 ng/g. Using the same test procedure to detect aflatoxin at 10,000 ng/g, the total variance was 264,719 (coefficient of variation of 5.1%). The sampling, sample preparation, and analytical steps accounted for 41, 57, and 2% of the total variance, respectively. A variance of 264,719 suggests that repeated test results will vary from 8,992 to 11,008 ng/g. Foods contaminated at low levels reflect a situation in which a small percentage of particles is contaminated and sampling becomes the largest source of uncertainty. Large samples are required to overcome the "needle-in-the-haystack" problem. Aflatoxin is easier to detect and identify in foods intentionally contaminated at high levels than in foods with low levels of contamination because the relative standard deviation (coefficient of variation) decreases and the percentage of contaminated kernels increases with an increase in concentration.

Aflatoxins↗

PubMed2006

Accounting for uncertainty in marine reserve design.

Ecosystems and the species and communities within them are highly complex systems that defy predictions with any degree of certainty. Managing and conserving these systems in the face of uncertainty remains a daunting challenge, particularly with respect to developing networks of marine reserves. Here we review several modelling frameworks that explicitly acknowledge and incorporate uncertainty, and then use these methods to evaluate reserve spacing rules given increasing levels of uncertainty about larval dispersal distances. Our approach finds similar spacing rules as have been proposed elsewhere - roughly 20-200 km - but highlights several advantages provided by uncertainty modelling over more traditional approaches to developing these estimates. In particular, we argue that uncertainty modelling can allow for (1) an evaluation of the risk associated with any decision based on the assumed uncertainty; (2) a method for quantifying the costs and benefits of reducing uncertainty; and (3) a useful tool for communicating to stakeholders the challenges in managing highly uncertain systems. We also argue that incorporating rather than avoiding uncertainty will increase the chances of successfully achieving conservation and management goals.

Conservation of Natural Resources↗

PubMedDate not supplied

Diagnostic tools to determine the quality of "transparent" regression-based QSARs: the "modelling power" plot.

A bivariate plot is presented for comparing two or more QSAR models. It is based on two new statistics associated with a regression model, the "descriptive power" (Dp), which is estimated through the relative uncertainty of model coefficients, and the "predictive power" (Pp), which is estimated through both the fitted and cross-validated explained variance of the response variable (i.e., biological activity). An algorithm was developed for performing equivalent multiple linear regression and partial-least-squares calculations. The results were validated by comparison with widely accepted commercial software. Dp and Pp statistics are defined to vary from 0 to 100%, so the modeler has a intuitive impression of the descriptive (i.e., global importance of the selected descriptors) and predictive (i.e., possibility of performing QSAR or just SAR estimations) power. These statistics represent a point in the Dp versus Pp "modelling power" plot, which facilitates visual multiple models comparison, but also could be used to substitute classical statistics and could even be combined to obtain a unique parameter to define (or compare) the model's quality.

Animals↗

PubMed2003

Predicting regional emissions and near-field air concentrations of soil fumigants using modest numerical algorithms: a case study using 1,3-dichloropropene.

Soil fumigants, used to control nematodes and crop disease, can volatilize from the soil application zone and into the atmosphere to create the potential for human inhalation exposure. An objective for this work is to illustrate the ability of simple numerical models to correctly predict pesticide volatilization rates from agricultural fields and to expand emission predictions to nearby air concentrations for use in the exposure component of a risk assessment. This work focuses on a numerical system using two U.S. EPA models (PRZM3 and ISCST3) to predict regional volatilization and nearby air concentrations for the soil fumigant 1,3-dichloropropene. New approaches deal with links to regional databases, seamless coupling of emission and dispersion models, incorporation of Monte Carlo sampling techniques to account for parametric uncertainty, and model input sensitivity analysis. Predicted volatility flux profiles of 1,3-dichloropropene (1,3-D) from soil for tarped and untarped fields were compared against field data and used as source terms for ISCST3. PRZM3 can successfully estimate correct order of magnitude regional soil volatilization losses of 1,3-D when representative regional input parameters are used (soil, weather, chemical, and management practices). Estimated 1,3-D emission losses and resulting air concentrations were investigated for five geographically diverse regions. Air concentrations (15-day averages) are compared with the current U.S. EPA's criteria for human exposure and risk assessment to determine appropriate setback distances from treated fields. Sensitive input parameters for volatility losses were functions of the region being simulated.

Air↗

PubMed1998

Protein construct storage: Bayesian variable selection and prediction with mixtures.

Determining optimal conditions for protein storage while maintaining a high level of protein activity is an important question in pharmaceutical research. A designed experiment based on a space-filling design was conducted to understand the effects of factors affecting protein storage and to establish optimal storage conditions. Different model-selection strategies to identify important factors may lead to very different answers about optimal conditions. Uncertainty about which factors are important, or model uncertainty, can be a critical issue in decision-making. We use Bayesian variable selection methods for linear models to identify important variables in the protein storage data, while accounting for model uncertainty. We also use the Bayesian framework to build predictions based on a large family of models, rather than an individual model, and to evaluate the probability that certain candidate storage conditions are optimal.

Bayes Theorem↗

PubMed2004

Uncertainty analysis in a mechanistic model of bacterial regrowth in distribution systems.

The first generation of mechanistic models of bacterial regrowth in distribution systems (DS) provides insight into cause-and-effect relationships. However, the state of knowledge about the processes included in these models is insufficient to warrant deterministic predictions. Even if the process descriptions are reasonable, the uncertainty in values of key system constants limits predictions of bacterial growth. A new mechanistic model was developed to incorporate the accepted knowledge of physical, chemical, and biological processes with the hydraulic features in order to capture the unsteady state behavior of the DS. Sensitivitytesting showed that the extent of bacterial regrowth was affected mainly by the rate constants for chlorine decay reactions in bulk water and on the pipe wall and by the maximum growth rate constant of attached bacteria. A simple hypothetical network was used to evaluate the effects of uncertainty in these three system constants by running 100 Monte Carlo simulations. Cumulative probability plots showed a wide range of predictions for concentrations of bacteria and chlorine in bulk water at various nodes in the DS. The magnitude of these concentrations and the range of values were greatly affected by water residence time to each node. Once the chlorine residual is depleted, bacterial growth is mainly influenced by the amount of substrate available. However, high values of the coefficients for the maximum growth rate of attached bacteria, the chlorine decay in bulk water, and the chlorine decay by wall reaction did not necessarily lead to the maximum bacterial growth at a given location.

Bacteria↗

PubMed2000

Efficient sensitivity/uncertainty analysis using the combined stochastic response surface method and automated differentiation: application to environmental and biological systems.

Estimation of uncertainties associated with model predictions is an important component of the application of environmental and biological models. "Traditional" methods for propagating uncertainty, such as standard Monte Carlo and Latin Hypercube Sampling, however, often require performing a prohibitive number of model simulations, especially for complex, computationally intensive models. Here, a computationally efficient method for uncertainty propagation, the Stochastic Response Surface Method (SRSM) is coupled with another method, the Automatic Differentiation of FORTRAN (ADIFOR). The SRSM is based on series expansions of model inputs and outputs in terms of a set of "well-behaved" standard random variables. The ADIFOR method is used to transform the model code into one that calculates the derivatives of the model outputs with respect to inputs or transformed inputs. The calculated model outputs and the derivatives at a set of sample points are used to approximate the unknown coefficients in the series expansions of outputs. A framework for the coupling of the SRSM and ADIFOR is developed and presented here. Two case studies are presented, involving (1) a physiologically based pharmacokinetic model for perchloroethylene for humans, and (2) an atmospheric photochemical model, the Reactive Plume Model. The results obtained agree closely with those of traditional Monte Carlo and Latin hypercube sampling methods, while reducing the required number of model simulations by about two orders of magnitude.

Animals↗

PubMed2004

Uncertainty and the value of diagnostic information, with application to axillary lymph node dissection in breast cancer.

In clinical decision making, it is common to ask whether, and how much, a diagnostic procedure is contributing to subsequent treatment decisions. Statistically, quantification of the value of the information provided by a diagnostic procedure can be carried out using decision trees with multiple decision points, representing both the diagnostic test and the subsequent treatments that may depend on the test's results. This article investigates probabilistic sensitivity analysis approaches for exploring and communicating parameter uncertainty in such decision trees. Complexities arise because uncertainty about a model's inputs determines uncertainty about optimal decisions at all decision nodes of a tree. We present the expected utility solution strategy for multistage decision problems in the presence of uncertainty on input parameters, propose a set of graphical displays and summarization tools for probabilistic sensitivity analysis in multistage decision trees, and provide an application to axillary lymph node dissection in breast cancer.

Axilla↗

PubMed2001

Identifiability and uncertainty analysis of the river water quality model no. 1 (RWQM1).

State of the art models as used in activated sludge modelling and recently proposed for river water quality modelling integrate the knowledge in a certain field. If applied to data from a specific site, such models are nearly always overparameterised. This raises the question of how many parameters can be fitted in a given context and how to find identifiable parameter subsets given the experimental layout. This problem is addressed for the kinetic parameters of a simplified version of the recently published river water quality model no. 1 (RWQM1). The selection of practically identifiable parameter subsets is discussed for typical boundary conditions as a function of the measurement layout. Two methods for identifiable subset selection were applied and lead to nearly the same results. Assuming upstream and downstream measurements of dissolved substances to be available, only a few (5-8) model parameters appear to be identifiable. Extensive measurement campaigns with dedicated experiments seem to be required for successful calibration of RWQM1. The estimated prior uncertainties of the model parameters are used to estimate the uncertainty of model predictions. Finally an estimate is provided for the maximum possible decrease in prediction uncertainty achievable by a perfect determination of the values of the identifiable model parameters.

Ammonia↗

PubMedDate not supplied

Estimation of markov chain transition probabilities and rates from fully and partially observed data: uncertainty propagation, evidence synthesis, and model calibration.

Markov transition models are frequently used to model disease progression. The authors show how the solution to Kolmogorov's forward equations can be exploited to map between transition rates and probabilities from probability data in multistate models. They provide a uniform, Bayesian treatment of estimation and propagation of uncertainty of transition rates and probabilities when 1) observations are available on all transitions and exact time at risk in each state (fully observed data) and 2) observations are on initial state and final state after a fixed interval of time but not on the sequence of transitions (partially observed data). The authors show how underlying transition rates can be recovered from partially observed data using Markov chain Monte Carlo methods in WinBUGS, and they suggest diagnostics to investigate inconsistencies between evidence from different starting states. An illustrative example for a 3-state model is given, which shows how the methods extend to more complex Markov models using the software WBDiff to compute solutions. Finally, the authors illustrate how to statistically combine data from multiple sources, including partially observed data at several follow-up times and also how to calibrate a Markov model to be consistent with data from one specific study.

Calibration↗

PubMed2003

Issues of replicability in Monte Carlo modeling: a case study with a pesticide leaching model.

Sensitivity and uncertainty analyses based on Monte Carlo sampling were undertaken for various numbers of runs of the pesticide leaching model (PELMO). Analyses were repeated 10 times with different seed numbers. The ranking of PELMO input parameters according to their influence on predictions for leaching was stable for the most influential parameters. For less influential parameters, the sensitivity ranking was severely influenced by the seed number used. For uncertainty analyses, probabilities of exceeding a particular concentration were significantly influenced by the seed number used in the random sampling of values for the two parameters considered, even for those cases in which 5,000 model runs were undertaken (coefficient of variation of 10 replicated analyses, 5%). A decrease in the variability of exceedance probabilities could be achieved by further increasing the number of model runs. However, this may prove to be impractical when complex deterministic models with a relatively long running time are used. Attention should be paid to replicability aspects by modelers when devising their approach to assessing the uncertainty associated with the modeling and by decision makers when examining the results of probabilistic approaches.

Environmental Monitoring↗

PubMed2006

Modeling the frequency and duration of microbial contamination events.

The frequency and duration of microbial contamination events in the environment in which ready-to-eat (RTE) foods are exposed for processing and packaging is subject to uncertainty and variability. Variability, within-model parameter uncertainty, and uncertainty regarding model selection are formally considered in modeling the frequency and duration of such contamination events by Listeria species. The estimated duration of contamination events represents a case where variability dominates with relatively little uncertainty about parameter values or model form. The estimated frequency of contamination events represents a case where there is not only substantial variability but also considerable within-model parameter uncertainty, as well as some uncertainty regarding model selection. The Bayesian Information Criterion provides a formal way of taking into account model uncertainty.

Animals↗

PubMed2004

Using sequential indicator simulation to assess the uncertainty of delineating heavy-metal contaminated soils.

Mapping the spatial distribution of soil pollutants is essential for delineating contaminated areas. Currently, geostatistical interpolation, kriging, is increasingly used to estimate pollutant concentrations in soils. The kriging-based approach, indicator kriging (IK), may be used to model the uncertainty of mapping. However, a smoothing effect is usually produced when using kriging in pollutant mapping. The detailed spatial patterns of pollutants could, therefore, be lost. The local uncertainty of mapping pollutants derived by the IK technique is referred to as the conditional cumulative distribution function (ccdf) for one specific location (i.e. single-location uncertainty). The local uncertainty information obtained by IK is not sufficient as the uncertainty of mapping at several locations simultaneously (i.e. multi-location uncertainty or spatial uncertainty) is required to assess the reliability of the delineation of contaminated areas. The simulation approach, sequential indicator simulation (SIS), which has the ability to model not only single, but also multi-location uncertainties, was used, in this study, to assess the uncertainty of the delineation of heavy metal contaminated soils. To illustrate this, a data set of Cu concentrations in soil from Taiwan was used. The results show that contour maps of Cu concentrations generated by the SIS realizations exhausted all the spatial patterns of Cu concentrations without the smoothing effect found when using the kriging method. Based on the SIS realizations, the local uncertainty of Cu concentrations at a specific location of x', refers to the probability of the Cu concentration z(x') being higher than the defined threshold level of contamination (z(c)). This can be written as Prob(SIS)[z(x')>z(c)], representing the probability of contamination. The probability map of Prob(SIS)[z(x')>z(c)] can then be used for delineating contaminated areas. In addition, the multi-location uncertainty of an area A,delineated as contaminated based on the probability map of Prob(SIS)[z(x')>z(c)], can be calculated to assess the reliability of delineation. Multi-location uncertainty refers to the probability of Cu concentrations in several locations, x'(1), x'(2), em leader, x'(m,) in the area A, being higher than the threshold (z(c)) as denoted by Prob(SIS)[z(x'(1))>z(c), z(x'(2))>z(c), em leader, andz(x'(m))>z(c)] or Prob(SIS)[z(A)>z(c)]. The multi-location uncertainty Prob(SIS)[z(A)>z(c)], obtained from the SIS, can be used to assess the reliability of delineation for regions suspected of contamination, (A), which has been delineated as contaminated. Reliance on this information facilitates the decision making process in determining which areas are contaminated and require cleanup action.

Copper↗

PubMed2000

Neural network model for predicting peak photochemical pollutant levels.

In this paper, an attempt is made for the 24-hr prediction of photochemical pollutant levels using a neural network model. For this purpose, a model is developed that relates peak pollutant concentrations to meteorological and emission variables and indexes. The analysis is based on measurements of O3 and NO2 from the city of Athens. The meteorological variables are selected to cover atmospheric processes that determine the fate of the airborne pollutants while special care is taken to ensure the availability of the required input data from routine observations or forecasts. The comparison between model predictions and actual observations shows a good agreement. In addition, a series of sensitivity tests is performed in order to evaluate the sensitivity of the model to the uncertainty in meteorological variables. Model forecasts are generally rather insensitive to small perturbations in most of the input meteorological data, while they are relatively more sensitive in changes in wind speed and direction.

Air Pollutants↗

PubMedDate not supplied

An investigation of numerical grid effects in parameter estimation.

Modern ground water characterization and remediation projects routinely require calibration and inverse analysis of large three-dimensional numerical models of complex hydrogeological systems. Hydrogeologic complexity can be prompted by various aquifer characteristics including complicated spatial hydrostratigraphy and aquifer recharge from infiltration through an unsaturated zone. To keep the numerical models computationally efficient, compromises are frequently made in the model development, particularly, about resolution of the computational grid and numerical representation of the governing flow equation. The compromise is required so that the model can be used in calibration, parameter estimation, performance assessment, and analysis of sensitivity and uncertainty in model predictions. However, grid properties and resolution as well as applied computational schemes can have large effects on forward-model predictions and on inverse parameter estimates. We investigate these effects for a series of one- and two-dimensional synthetic cases representing saturated and variably saturated flow problems. We show that "conformable" grids, despite neglecting terms in the numerical formulation, can lead to accurate solutions of problems with complex hydrostratigraphy. Our analysis also demonstrates that, despite slower computer run times and higher memory requirements for a given problem size, the control volume finite-element method showed an advantage over finite-difference techniques in accuracy of parameter estimation for a given grid resolution for most of the test problems.

Calibration↗

PubMed2005

Accounting for both random errors and systematic errors in uncertainty propagation analysis of computer models involving experimental measurements with Monte Carlo methods.

A Monte Carlo method is presented to study the effect of systematic and random errors on computer models mainly dealing with experimental data. It is a common assumption in this type of models (linear and nonlinear regression, and nonregression computer models) involving experimental measurements that the error sources are mainly random and independent with no constant background errors (systematic errors). However, from comparisons of different experimental data sources evidence is often found of significant bias or calibration errors. The uncertainty analysis approach presented in this work is based on the analysis of cumulative probability distributions for output variables of the models involved taking into account the effect of both types of errors. The probability distributions are obtained by performing Monte Carlo simulation coupled with appropriate definitions for the random and systematic errors. The main objectives are to detect the error source with stochastic dominance on the uncertainty propagation and the combined effect on output variables of the models. The results from the case studies analyzed show that the approach is able to distinguish which error type has a more significant effect on the performance of the model. Also, it was found that systematic or calibration errors, if present, cannot be neglected in uncertainty analysis of models dependent on experimental measurements such as chemical and physical properties. The approach can be used to facilitate decision making in fields related to safety factors selection, modeling, experimental data measurement, and experimental design.

Journal Article↗

PubMed2001

Description of a generally applicable model for the evaluation of uncertainty of measurement in clinical chemistry.

There is a growing pressure on clinical chemistry laboratories to conform to quality standards that require the evaluation and expression of the uncertainty of results of measurement. Nevertheless, there is some reluctance to accept the uncertainty concept in the analytical community due to difficulty in evaluating uncertainty in practice. For example, often the uncertainty of some uncertainty components is not known very well in clinical chemistry measurements, such as those associated with matrix effects or with the values of the calibrators. Moreover, it is not clear how to interpret uncertainty in relation to diagnostic criteria, reference ranges and other decision limits in clinical chemistry practice. Hence, the value of reporting the uncertainty of the measurement result is not obvious. In this paper it is suggested a relatively simple, logical procedure for evaluating measurement uncertainty based on the principles in the Guide for the Expression of Uncertainty of Measurement (GUM). The measurement process is partitioned into elements that are well known to the analyst, namely sampling, calibration, and analysis. The corresponding model function expresses the result of a measurement as the value obtained by the analytical procedure multiplied by the correction factors for sampling bias, for bias caused by the calibrators, and for other types of bias. Under normal conditions, when the measurement procedure is validated and corrected for all known bias, the expected value of each correction factor is one. The uncertainty that remains with regard to sampling, manufacturing of calibrators and other types of bias is combined with the analytical imprecision to yield a combined uncertainty of a result of measurement. The advantages of this approach are: (i) Data from the method validation, internal quality control and from participation in external quality control schemes can be used as input in the uncertainty evaluation process. (ii) The partition of the measurement into well-defined tasks highlights the different responsibilities of the clinical chemistry laboratory and of the manufacturer of reagents and calibrators. (iii) The approach can be used to harmonize the uncertainty evaluation process, which is particularly relevant for laboratories seeking accreditation under ISO 17025. The application of the proposed model is demonstrated by evaluating the uncertainty of a result of a measurement of prolactin in human serum. In the example it is shown how to treat the uncertainty associated with a calibrator supplied with a commercial analytical kit, and how to evaluate the uncertainty associated with matrix effects.

Bias↗