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Results for “Uncertainty modelling”

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PubMed2005

Interval fuzzy modeling applied to Wiener models with uncertainties.

This correspondence addresses the problem of interval fuzzy model identification and its use in the case of the robust Wiener model. The method combines a fuzzy identification methodology with some ideas from linear programming theory. On a finite set of measured data, an optimality criterion which minimizes the maximum estimation error between the data and the proposed fuzzy model output is used. The min-max optimization problem can then be seen as a linear programming problem that is solved to estimate the parameters of the fuzzy model in each fuzzy domain. This results in lower and upper fuzzy models that define the confidence interval of the observed data. The model is called the interval fuzzy model and is used to approximate the static nonlinearity in the case of the Wiener model with uncertainties. The resulting model has the potential to be used in the areas of robust control and fault detection.

Algorithms↗

PubMedDate not supplied

Multimodel ranking and inference in ground water modeling.

Uncertainty of hydrogeologic conditions makes it important to consider alternative plausible models in an effort to evaluate the character of a ground water system, maintain parsimony, and make predictions with reasonable definition of their uncertainty. When multiple models are considered, data collection and analysis focus on evaluation of which model(s) is(are) most supported by the data. Generally, more than one model provides a similar acceptable fit to the observations; thus, inference should be made from multiple models. Kullback-Leibler (K-L) information provides a rigorous foundation for model inference that is simple to compute, is easy to interpret, selects parsimonious models, and provides a more realistic measure of precision than evaluation of any one model or evaluation based on other commonly referenced model selection criteria. These alternative criteria strive to identify the true (or quasi-true) model, assume it is represented by one of the models in the set, and given their preference for parsimony regardless of the available number of observations the selected model may be underfit. This is in sharp contrast to the K-L information approach, where models are considered to be approximations to reality, and it is expected that more details of the system will be revealed when more data are available. We provide a simple, computer-generated example to illustrate the procedure for multimodel inference based on K-L information and present arguments, based on statistical underpinnings that have been overlooked with time, that its theoretical basis renders it preferable to other approaches.

Evaluation Studies as Topic↗

PubMed2004

Incorporating model parameter uncertainty into inverse treatment planning.

Radiobiological treatment planning depends not only on the accuracy of the models describing the dose-response relation of different tumors and normal tissues but also on the accuracy of tissue specific radiobiological parameters in these models. Whereas the general formalism remains the same, different sets of model parameters lead to different solutions and thus critically determine the final plan. Here we describe an inverse planning formalism with inclusion of model parameter uncertainties. This is made possible by using a statistical analysis-based frameset developed by our group. In this formalism, the uncertainties of model parameters, such as the parameter a that describes tissue-specific effect in the equivalent uniform dose (EUD) model, are expressed by probability density function and are included in the dose optimization process. We found that the final solution strongly depends on distribution functions of the model parameters. Considering that currently available models for computing biological effects of radiation are simplistic, and the clinical data used to derive the models are sparse and of questionable quality, the proposed technique provides us with an effective tool to minimize the effect caused by the uncertainties in a statistical sense. With the incorporation of the uncertainties, the technique has potential for us to maximally utilize the available radiobiology knowledge for better IMRT treatment.

Algorithms↗

PubMed2004

Multimedia fate model for hexachlorocyclohexane in Tianjin, China.

A level III fugacity model was applied to characterize the fate of gamma-HCH in Tianjin, China, before the 1990s when the contamination reached its maximum at steady state. Geometric means were used as model inputs. The concentrations of gamma-HCH in air, surface water, soil, sediment, crops, and fish as well as transfer fluxes across the interface between the compartments were derived under the assumption of steady state. The calculated concentrations were validated by independent data collected from the literature. There was generally good agreement between the estimated and the observed concentrations, and the differences were all less than 0.6 log units for air, water, soil, sediment, and fish and approximately 1 order of magnitude for crops. Around 97% of gamma-HCH accumulated in soil and sediment. Wastewater irrigation was not an important pathway for delivering gamma-HCH to soil as compared to the dominant source of agricultural application. Degradation and advective airflow carried much gamma-HCH out of the system. Sensitivities of the model estimates to input parameters were tested, and a coefficient of variation normalized sensitivity coefficient was defined for the test. The most influential parameters were degradation rates in sediment and soil, application rates, concentrations in wastewater, and adsorption coefficients. Monte Carlo simulation was conducted for model uncertainty analysis. The model was run 20 000 times using randomly generated data from predefined log-normal distribution density functions. All calculated concentrations and fluxes were log-normally distributed. The dispersions of the calculated and observed concentrations were compared in terms of coefficients of variation to distinguish between true variability and model uncertainty.

Air↗

PubMed2003

Testing the mediating effect of appraisal in the model of uncertainty in illness study.

BACKGROUND: Although there have been a great number of research studies based on the model of uncertainty in illness, few studies have considered the appraisal portion of model. PURPOSE: The purpose of this study was to test the mediating effect of appraisal in the model of uncertainty in illness. Additionally, this study aimed to examine the relationships among uncertainty, symptom severity, appraisal, and anxiety in patients newly diagnosed with atrial fibrillation. METHODS: This study employed a descriptive correlational and cross-sectional survey design using a face-to-face interview method. Patients diagnosed with atrial fibrillation within the previous 6 months prior to data collection were interviewed by Mishel Uncertainty in Illness Scale-Community Form, appraisal scale, Symptom Checklist-Severity V.3, and State Anxiety Inventory. RESULTS: A total of 81 patients with atrial fibrillation were recruited from two large urban medical centers in Cleveland, Ohio, U.S.A. Symptom severity was the significant variable in explaining uncertainty (beta=0.34). Individuals with greater symptom severity perceived more uncertainty. Uncertainty was appraised as a danger rather than opportunity, and those with greater uncertainty appraised a greater danger (p<.01). While the appraisal of opportunity had the negative relationship with anxiety (r=-0.25), the appraisal of danger was positively associated with anxiety (r=0.78). The measure of goodness of fit (Q) of the model was.7863, and the significant test (chi(2)) for the Q was statistically significant (df =3, p<.001). Accordingly, the overall mediating model of uncertainty in illness was proven not to be fit to the empirical data of patients with atrial fibrillation. Consequently, the mediating effect of appraisal was not supported by the empirical data of this study. CONCLUSION: The findings of this study were discussed in terms of their relevance compared with those of previous studies or theoretical framework and the plausible explanations on study findings. Lastly, in order to expand the present body of knowledge on uncertainty in illness model, recommendations for the future nursing studies were included.

Journal Article↗

PubMed2001

Maximum entropy approach for modeling random uncertainties in transient elastodynamics.

A new approach is presented for analyzing random uncertainties in dynamical systems. This approach consists of modeling random uncertainties by a nonparametric model allowing transient responses of mechanical systems submitted to impulsive loads to be predicted in the context of linear structural dynamics. The information used does not require the description of the local parameters of the mechanical model. The probability model is deduced from the use of the entropy optimization principle, whose available information is constituted of the algebraic properties related to the generalized mass, damping, and stiffness matrices which have to be positive-definite symmetric matrices, and the knowledge of these matrices for the mean reduced matrix model. An explicit construction and representation of the probability model have been obtained and are very well suited to algebraic calculus and to Monte Carlo numerical simulation in order to compute the transient responses of structures submitted to impulsive loads. The fundamental properties related to the convergence of the stochastic solution with respect to the dimension of the random reduced matrix model are analyzed. Finally, an example is presented.

Journal Article↗

PubMed1997

Uncertainty in hydrogeological modelling.

Hydrogeological models are built to predict groundwater flow and the fate of contaminants in the subsurface. After the crucial step of building a conceptual model that includes the processes that should be accounted for, parameter values must be assigned to the components of the model. Measured values of these parameters are available only at a few locations, as is the case for transmissivity, hydraulic conductivity or porosity. Therefore, before making predictions about the movement of contaminants in the aquifer, it is necessary to predict the parameter values at unsampled locations. Given the spatial heterogeneity of the parameters involved, this prediction is always uncertain. Model parameter uncertainty propagates to flow-response variables and further to transport predictions. Parameter uncertainty can be modelled using stochastic methods. Stochastic simulation is used for the generation of alternative spatial realizations of the parameter values, which are then used as input to groundwater flow and mass transport models to obtain frequency distributions of the response variables, e.g. flow velocities, arrival times or concentration levels. These frequency distributions help in making risk-qualified decisions. In order to make these frequency distributions as precise and accurate as possible, it is necessary to incorporate all relevant information in the parameter uncertainty model, i.e. it is necessary to condition the parameter realizations to all direct and indirect information. With this aim, new techniques have recently been developed in hydrogeological modelling. One such technique, for the generation of conductivity realizations conditioned to conductivity, piezometric head and geophysical data, is the self-calibrated method.

Calibration↗

PubMed2005

Combined effects of uncertainty and organizational justice on employee health: testing the uncertainty management model of fairness judgments among Finnish public sector employees.

We examined whether the combination of uncertainty (lack of work-time control, and negative changes at work) and organizational justice (i.e., justice of decision-making procedures and interpersonal treatment at work) contributes to sickness absence. A total of 7083 male and 24,317 female Finnish public sector employees completed questionnaires designed to assess organizational justice, workload and other factors. Hierarchical regression showed that after adjustment for age, income, and health behaviors low procedural and interactional justice were related to long sickness absence spells. In accordance with the uncertainty management model, these associations were dependent on experienced work-time control and perceived changes at work.

Adult↗

PubMedDate not supplied

Influence of autoregressive model parameter uncertainty on spectral estimates of heart rate dynamics.

Linear autoregressive (AR) model-based heart rate (HR) spectral analysis has been widely used to study HR dynamics. Owing to system and measurement noise, the parameters of an AR model have intrinsic statistical uncertainty. In this study, we evaluate how this AR parameter uncertainty can translate to uncertainty in HR power spectra. HR time series, obtained from seven subjects in supine and standing positions, were fitted to AR models by least squares minimization via singular value decomposition. Spectral uncertainty due to inexact parameter estimation was assessed through a Monte Carlo study in which the AR model parameters were varied randomly according to their Gaussian distributions. Histogram techniques were used to evaluate the distribution of 50,000 AR spectral estimates of each HR time series. These Monte Carlo uncertainties were found to exceed those predicted by previous theoretical approximations. It was determined that the uncertainty of AR HR spectral estimates, particularly the locations and magnitudes of spectral peaks, can often be large. The same Monte Carlo analysis was applied to synthetic AR time series and found levels of spectral uncertainty similar to that of the HR data, thus suggesting that the results of this study are not specific to experimental HR data. Therefore, AR spectra may be unreliable, and one must be careful in assigning pathophysiological origins to specific spectral features of any one spectrum.

Adult↗

PubMed2005

Radionuclides in fruit systems: model-model intercomparison study.

Modeling is widely used to predict radionuclide distribution following accidental radionuclide releases. Modeling is crucial in emergency response planning and risk communication, and understanding model uncertainty is important not only in conducting analysis consistent with current regulatory guidance, but also in gaining stakeholder and decision-maker trust in the process and confidence in the results. However, while methods for dealing with parameter uncertainty are fairly well developed, an adequate representation of uncertainties associated with models remains rare. This paper addresses uncertainty about a model's structure (i.e., the relevance of simplifying assumptions and mathematical equations) that is seldom addressed in practical applications of environmental modeling. The use of several alternative models to derive a range of model outputs or risks is probably the only available technique to assess consistency in model prediction. Since each independent model requires significant resources for development and calibration, multiple models are not generally applied to the same problem. This study uses results from one such model intercomparison conducted by the Fruits Working Group, which was created under the International Atomic Energy Agency (IAEA) BIOMASS (BIOsphere Modelling and ASSessment) Program. Model-model intercomparisons presented in this study were conducted by the working group for two different scenarios (acute or continuous deposition), one radionuclide ((137)Cs), and three fruit-bearing crops (strawberries, apples, and blackcurrants). The differences between models were as great as five orders of magnitude for short-term predictions following acute radionuclide deposition. For long-term predictions and for the continuous deposition scenario, the differences between models were about two orders of magnitude. The difference between strawberry, apple, and blackcurrant contamination predicted by one model is far less than the difference in prediction of contamination for a single plant species given by different models. This study illustrates the importance of problem formulation and implementation of an analytic-deliberative process in risk characterization.

Cesium Radioisotopes↗

PubMed2000

Modeling the uncertainty of surgical procedure times: comparison of log-normal and normal models.

BACKGROUND: Medical institutions are under increased economic pressure to schedule elective surgeries efficiently to contain the costs of surgical services. Surgical scheduling is complicated by variability inherent in the duration of surgical procedures. Modeling that variability, in turn, provides a mechanism to generate accurate time estimates. Accurate time estimates are important operationally to improve operating room utilization and strategically to identify surgeons, procedures, or patients whose duration of surgeries differ from what might be expected. METHODS: The authors retrospectively studied 40,076 surgical cases (1,580 Current Procedural Terminology-anesthesia combinations, each with a case frequency of five or more) from a large teaching hospital, and attempted to determine whether the distribution of surgical procedure times more closely fit a normal or a log-normal distribution. The authors tested goodness-of-fit to these data for both models using the Shapiro-Wilk test. Reasons, in practice, the Shapiro-Wilk test may reject the fit of a log-normal model when in fact it should be retained were also evaluated. RESULTS: The Shapiro-Wilk test indicates that the log-normal model is superior to the normal model for a large and diverse set of surgeries. Goodness-of-fit tests may falsely reject the log-normal model during certain conditions that include rounding errors in procedure times, large sample sizes, untrimmed outliers, and heterogeneous mixed populations of surgical procedure times. CONCLUSIONS: The authors recommend use of the log-normal model for predicting surgical procedure times for Current Procedural Terminology-anesthesia combinations. The results help to legitimize the use of log transforms to normalize surgical procedure times before hypothesis testing using linear statistical models or other parametric statistical tests to investigate factors affecting the duration of surgeries.

Databases, Factual↗

PubMed2003

Influences of parameter uncertainties within the ICRP-66 respiratory tract model: a parameter sensitivity analysis.

An important aspect in model uncertainty analysis is the evaluation of input parameter sensitivities with respect to model outcomes. In previous publications, parameter uncertainties were examined for the ICRP-66 respiratory tract model. The studies were aided by the development and use of a computer code LUDUC (Lung Dose Uncertainty Code) which allows probabilities density functions to be specified for all ICRP-66 model input parameters. These density functions are sampled using Latin hypercube techniques with values subsequently propagated through the ICRP-66 model. In the present study, LUDUC has been used to perform a detailed parameter sensitivity analysis of the ICRP-66 model using input parameter density functions specified in previously published articles. The results suggest that most of the variability in the dose to a given target region is explained by only a few input parameters. For example, for particle diameters between 0.1 and 50 microm, about 50% of the variability in the total lung dose (weighted sum of target tissue doses) for 239PuO2 is due to variability in the dose to the alveolar-interstitial (AI) region. In turn, almost 90% of the variability in the dose to the AI region is attributable to uncertainties in only four parameters in the model: the ventilation rate, the AI deposition fraction, the clearance rate constant for slow-phase absorption of deposited material to the blood, and the clearance rate constant for particle transport from the AI2 to bb1 compartment. A general conclusion is that many input parameters do not significantly influence variability in final doses. As a result, future research can focus on improving density functions for those input variables that contribute the most to variability in final dose values.

Absorption↗

PubMed2001

Multinomial analysis of smoothed HIV back-calculation models incorporating uncertainty in the AIDS incidence.

Back-calculation models, developed to reconstruct the past trend of human immunodeficiency virus (HIV) and to project future acquired immunodeficiency syndrome incidence (AIDS), are usually and unrealistically based on the assumption that the observed AIDS counts are independently distributed according to a Poisson process. In contrast, we argue that a multinomial framework is more suitable to this situation, leading to a natural covariance structure. The ill-conditioned nature of the problem is solved by modelling the HIV parameters according to a cubic spline function to reduce the dimensionality of the parameter space and obtain smoother parameter estimates. We applied a regression spline technique which yields to a computationally stable basis incorporating the incubation period in the new design matrix. We directly incorporate the reporting delay distribution in the AIDS incidence data, leading to a more complex formulation of the variance and covariance model that is adapted to the iteratively reweighted least square (IRLS) algorithm. In this case we obtain more accurate estimates of the standard error of the HIV incidence, especially in the most recent time. Our model, which uses a cubic spline reparameterization based on a multinomial probability distribution, is applied to the AIDS epidemic data in Italy.

Acquired Immunodeficiency Syndrome↗

PubMed2025

Modeling unknowns: A vision for uncertainty-aware machine learning in healthcare.

The integration of machine learning (ML) into healthcare is accelerating, driven by the proliferation of biomedical data and the promise of data-driven clinical support. A key challenge in this context is managing the pervasive uncertainty inherent in medical reasoning and decision-making. Despite its recognized importance, uncertainty is often underrepresented in the design and evaluation of clinical AI systems. Here we report an editorial overview of a special issue dedicated to uncertainty modeling in medical AI, which gathers theoretical, methodological, and practical contributions addressing this critical gap. Across these works, authors reveal that fewer than 4% of studies address uncertainty explicitly, and propose alternative design principles-such as optimizing for clinical net benefit or embedding explainability with confidence estimates. Notable contributions include the RelAI system for real-time prediction reliability, empirical findings on how uncertainty communication shapes clinical interpretation, and benchmarks for out-of-distribution detection in tabular data. Furthermore, this issue highlights the use of causal reasoning and anomaly detection to enhance system robustness and accountability. Together, these studies argue that representing, communicating, and operationalizing uncertainty are essential not only for clinical safety but also for building trust in AI-driven care. This special issue thus repositions uncertainty from a limitation to a foundational asset in the responsible deployment of ML in healthcare.

Machine Learning↗

PubMed1985

Uncertainty explains many aspects of visual contrast detection and discrimination.

More than 20 years ago, Tanner [Ann. N.Y. Acad. Sci. 89, 752 (1961)] noted that observers asked to detect a signal act as though they are uncertain about the physical characteristics of the signal to be detected. The popular assumptions of probability summation and decision variable, taken together, imply this uncertainty. This paper defines and uncertainty model of visual detection that assumes that the observer is uncertain among many signals and chooses the likeliest. With only four parameters, the uncertainty model explains why d' is approximately a power function of contrast ("nonlinear transduction") and accurately predicts effects of summation, facilitation, noise, subjective criterion, and task for near-threshold contrast. Thus the uncertainty model offers a synthesis of much of our current understanding of visual contrast detection and discrimination.

Attention↗

PubMed2004

Robust sparse hyperplane classifiers: application to uncertain molecular profiling data.

Molecular profiling studies can generate abundance measurements for thousands of transcripts, proteins, metabolites, or other species in, for example, normal and tumor tissue samples. Treating such measurements as features and the samples as labeled data points, sparse hyperplanes provide a statistical methodology for classifying data points into one of two categories (classification and prediction) and defining a small subset of discriminatory features (relevant feature identification). However, this and other extant classification methods address only implicitly the issue of observed data being a combination of underlying signals and noise. Recently, robust optimization has emerged as a powerful framework for handling uncertain data explicitly. Here, ideas from this field are exploited to develop robust sparse hyperplanes, i.e., classification and relevant feature identification algorithms that are resilient to variation in the data. Specifically, each data point is associated with an explicit data uncertainty model in the form of an ellipsoid parameterized by a center and covariance matrix. The task of learning a robust sparse hyperplane from such data is formulated as a second order cone program (SOCP). Gaussian and distribution-free data uncertainty models are shown to yield SOCPs that are equivalent to the SCOP based on ellipsoidal uncertainty. The real-world utility of robust sparse hyperplanes is demonstrated via retrospective analysis of breast cancer related transcript profiles. Data-dependent heuristics are used to compute the parameters of each ellipsoidal data uncertainty model. The generalization performance of a specific implementation, designated "robust LIKNON," is better than its nominal counterpart. Finally, the strengths and limitations of robust sparse hyperplanes are discussed.

Breast Neoplasms↗

PubMed2002

Validation of pesticide root zone model 3.12: employing uncertainty analysis.

Computer models are being increasingly used to provide an efficient cost-effective means of evaluating the fate and behavior of chemicals in the environment. These models can be used in lieu of or in conjunction with field studies. Because of the increasing reliance on models for critical regulatory decision making, the need arose to assess the validity of regulatory models via an analysis of the correlation of model response estimates with measured data. In conjunction with the evaluation of the correlation of model response estimates and measured field data, a rigorous statistically based validation was also warranted. Because of the unique nature of the correlative exercise using modeled and measured data, standard statistical analyses, while informative, failed to encompass factors associated with the uncertainty of measured environmental fate data and potential model inputs. In an effort to evaluate this uncertainty, an initial sensitivity analysis was performed where key model input parameters for runoff and leaching simulations were identified. Once the sensitive input parameters were identified, a Monte Carlo-based preprocessor was developed whereby the sampling distributions of these parameters were used to propagate uncertainty in the input parameters into error in model predictions. Importantly, assumptions about parameter distributions for input into the Monte Carlo tool were made only after a formal detailed site-specific analysis of measured field data. Employing the functionality of the Crystal Ball Pro development environment, the pesticide root zone model (PRZM) 3.12 was run iteratively for 500 trials, and model output was collated and analyzed. The model predictions were considered reasonably accurate for most regulatory requirements, and the model prediction error was considered acceptable.

Decision Making↗

PubMed2003

Limitations of a convolution method for modeling geometric uncertainties in radiation therapy. I. The effect of shift invariance.

Convolution methods have been used to model the effect of geometric uncertainties on dose delivery in radiation therapy. Convolution assumes shift invariance of the dose distribution. Internal inhomogeneities and surface curvature lead to violations of this assumption. The magnitude of the error resulting from violation of shift invariance is not well documented. This issue is addressed by comparing dose distributions calculated using the Convolution method with dose distributions obtained by Direct Simulation. A comparison of conventional Static dose distributions was also made with Direct Simulation. This analysis was performed for phantom geometries and several clinical tumor sites. A modification to the Convolution method to correct for some of the inherent errors is proposed and tested using example phantoms and patients. We refer to this modified method as the Corrected Convolution. The average maximum dose error in the calculated volume (averaged over different beam arrangements in the various phantom examples) was 21% with the Static dose calculation, 9% with Convolution, and reduced to 5% with the Corrected Convolution. The average maximum dose error in the calculated volume (averaged over four clinical examples) was 9% for the Static method, 13% for Convolution, and 3% for Corrected Convolution. While Convolution can provide a superior estimate of the dose delivered when geometric uncertainties are present, the violation of shift invariance can result in substantial errors near the surface of the patient. The proposed Corrected Convolution modification reduces errors near the surface to 3% or less.

Algorithms↗