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Some theory problems affecting parameter estimation are discussed in this paper. Influence and transformation between errors of stochastic and functional models is pointed out as well. For choosing the best adjustment model, a for...
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Some theory problems affecting parameter estimation are discussed in this paper. Influence and transformation between errors of stochastic and functional models is pointed out as well. For choosing the best adjustment model, a formula, which is different from the literatures existing methods, for estimating and identifying the model error, is proposed. On the basis of the proposed formula, an effective approach of selecting the best model of adjustment system is given.
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The state of the art of the research on modelling of analog-to-digital converter (ADC)-based measuring devices is surveyed. Main topics of modelling are reviewed according to the fields of prevailing scientific interest in metrolo...
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The state of the art of the research on modelling of analog-to-digital converter (ADC)-based measuring devices is surveyed. Main topics of modelling are reviewed according to the fields of prevailing scientific interest in metrological research such as quantization models, error models, and correction-aimed models. In these fields, recent developments are analysed with the aim of focusing both the contemporary situation and the imminent trends.
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Three statistical models for the forecast errors for inflow into the Langvatn reservoir in Northern Norway have been constructed and tested according to the agreement between (i) the forecast distribution and the observations and ...
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Three statistical models for the forecast errors for inflow into the Langvatn reservoir in Northern Norway have been constructed and tested according to the agreement between (i) the forecast distribution and the observations and (ii) median values of the forecast distribution and the observations. For the first model observed and forecasted inflows were transformed by the Box-Cox transformation before a first order auto-regressive model was constructed for the forecast errors. The parameters were conditioned on weather classes. In the second model the Normal Quantile Transformation (NQT) was applied on observed and forecasted inflows before a similar first order auto-regressive model was constructed for the forecast errors. For the third model positive and negative errors were modeled separately. The errors were first NQT-transformed before conditioning the mean error values on climate, forecasted inflow and yesterday's error. To test the three models we applied three criterions: we wanted (a) the forecast distribution to be reliable; (b) the forecast intervals to be narrow; (c) the median values of the forecast distribution to be close to the observed values. Models 1 and 2 gave almost identical results. The median values improved the forecast with Nash-Sutcliffe R-eff increasing from 0.77 for the original forecast to 0.87 for the corrected forecasts. Models 1 and 2 over-estimated the forecast intervals but gave the narrowest intervals. Their main drawback was that the distributions are less reliable than Model 3. For Model 3 the median values did not fit well since the auto-correlation was not accounted for. Since Model 3 did not benefit from the potential variance reduction that lies in bias estimation and removal it gave on average wider forecasts intervals than the two other models. At the same time Model 3 on average slightly under-estimated the forecast intervals, probably explained by the use of average measures to evaluate the fit.
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State-space production models are increasingly being used in fisheries stock assessment as they provide the ability to account for observation and process errors. However, model performance when the population dynamics specified d...
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State-space production models are increasingly being used in fisheries stock assessment as they provide the ability to account for observation and process errors. However, model performance when the population dynamics specified differs from the true biological process requires evaluation. We compared the estimation performance of a standard observation-error approach with a state-space production model for various simulated levels of model, process, and observation errors. We found that the state-space production model was generally superior to the observation-error estimator. However, the advantage of the state-space production model in parameter estimation diminished with increased model errors. The observation-error estimator outperformed the state-space production model when model error exceeded a certain level. A significant number of small process and observation error estimates (< 0.0001) from the state-space model were observed. The process and observation error estimates were biased, with the bias direction influenced by the ratio of process error to observation error. Our results highlight precautions in applying different types of production model estimators in fisheries stock assessment and management.
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In order to accurately identify the thermally induced positioning errors, an improved measurement method is proposed based on the repeatability of a machine tool's temperature rise process. Using this improved measurement method, ...
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In order to accurately identify the thermally induced positioning errors, an improved measurement method is proposed based on the repeatability of a machine tool's temperature rise process. Using this improved measurement method, the mismatches between the thermally induced positioning errors and the machine temperatures can effectively be avoided. To improve the modeling accuracy and efficiency, the least-square fitting of orthogonal polynomial method is used in this research. Using this error modeling method, the thermally induced positioning errors are fitted by 96.7 %. To realize the thermally induced positioning error compensation, a new error compensation method is proposed based on the network. Experimental results show that the thermally induced positioning errors are compensated by 92.6 % compared with no compensation.
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Interest in the computational aspects ofmodeling has been steadily growing in philosophy of science. This paper aims to advance the discussion by articulating the way in which modeling and computational errors are related and by e...
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Interest in the computational aspects ofmodeling has been steadily growing in philosophy of science. This paper aims to advance the discussion by articulating the way in which modeling and computational errors are related and by explaining the significance of error management strategies for the rational reconstruction of scientific practice. To this end, we first characterize the role and nature of modeling error in relation to a recipe for model construction known as Euler’s recipe. We then describe a general model that allows us to assess the quality of numerical solutions in terms of measures of computational errors that are completely interpretable in terms of modeling error. Finally, we emphasize that this type of error analysis involves forms of perturbation analysis that go beyond the basic model-theoretical and statistical/ probabilistic tools typically used to characterize the scientific method; this demands that we revise and complement our reconstructive toolbox in a way that can affect our normative image of science.
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This paper presents the quantification of numerical and modelling errors for the solution of the flow around the KVLCC2 tanker at model-scale Reynolds number. Numerical errors are also quantified for full-scale Reynolds number sim...
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This paper presents the quantification of numerical and modelling errors for the solution of the flow around the KVLCC2 tanker at model-scale Reynolds number. Numerical errors are also quantified for full-scale Reynolds number simulations to address the numerical accuracy of the prediction of scale-effects. The calculations are performed with the solver ReFRESCO using fourteen distinct Reynolds-Averaged Navier-Stokes (RANS) equations models. The quantities of interest for the Validation exercises at model-scale are the resistance coefficient and the velocity and turbulence kinetic energy fields at the propeller plane. Modelling errors are estimated using the ASME V & V20 procedure which requires numerical and experimental data with their respective uncertainties. Numerical uncertainties are dominated by the contribution of the discretization error, which is determined by grid refinement studies. Scale-effects are also assessed for the wake-fraction and form factor. The outcome shows that quantifying modelling errors is not a trivial exercise that depends on the quality and details of simulations and experiments. Nonetheless, it is also evident that a quantitative evaluation of modelling errors is more reliable than traditional graphical comparisons of simulations and experiments. Full-scale results show scale-effects larger than numerical uncertainties that are illustrated for the form-factor and wake-fraction.
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The effect of systematic model error on the model predictions varies in space and time, and differs for the flow and solute transport components of a groundwater model. The classical single-objective formulation of the inverse pro...
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The effect of systematic model error on the model predictions varies in space and time, and differs for the flow and solute transport components of a groundwater model. The classical single-objective formulation of the inverse problem by its nature cannot capture these characteristics of model error. We introduce an inverse approach that allows the spatial and temporal variability of model error to be evaluated in the parameter space. A set of solutions for model parameters are obtained by this new method that almost exactly satisfies the model equation at each observation point (per-datum calibration). This set of parameter estimates are then used to define a posterior parameter space that may be translated into a probabilistic description of model output to represent the level of confidence in model performance. It is shown that this approach can provide useful information regarding the strengths and limitations of a model as well as the performance of classical calibration procedures.
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Introduction: In pharmacokinetic modelling, a combined proportional and additive residual error model is often preferred over a proportional or additive residual error model. Different approaches have been proposed, but a comparis...
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Introduction: In pharmacokinetic modelling, a combined proportional and additive residual error model is often preferred over a proportional or additive residual error model. Different approaches have been proposed, but a comparison between approaches is still lacking.
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Abstract Introduction In pharmacokinetic modelling, a combined proportional and additive residual error model is often preferred over a proportional or additive residual error model. Different approaches have been proposed, but a ...
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Abstract Introduction In pharmacokinetic modelling, a combined proportional and additive residual error model is often preferred over a proportional or additive residual error model. Different approaches have been proposed, but a comparison between approaches is still lacking. Methods The theoretical background of the methods is described. Method VAR assumes that the variance of the residual error is the sum of the statistically independent proportional and additive components; this method can be coded in three ways. Method SD assumes that the standard deviation of the residual error is the sum of the proportional and additive components. Using datasets from literature and simulations based on these datasets, the methods are compared using NONMEM. Results The different coding of methods VAR yield identical results. Using method SD, the values of the parameters describing residual error are lower than for method VAR, but the values of the structural parameters and their inter-individual variability are hardly affected by the choice of the method. Conclusion Both methods are valid approaches in combined proportional and additive residual error modelling, and selection may be based on OFV. When the result of an analysis is used for simulation purposes, it is essential that the simulation tool uses the same method as used during analysis. Graphical Abstract Display Omitted
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