Evaluating Estimated Parameter Values and Parameter Uncertainty

2007 ◽  
pp. 124-157 ◽  
Keyword(s):  
Parameter Uncertainty ◽  
Parameter Values

Sensitivity Analysis

2021 ◽  
pp. 251-262
Author(s):  
Timothy E. Essington
Keyword(s):  
Sensitivity Analysis ◽  
Parameter Uncertainty ◽  
Monte Carlo Analysis ◽  
Interactive Effects ◽  
Structure Parameter ◽  
Ecological Processes ◽  
Individual Parameter ◽  
Global Sensitivity ◽  
Versus Parameter ◽  
Parameter Values

The chapter “Sensitivity Analysis” reviews why sensitivity analysis is a critical component of mathematical modeling, and the different ways of approaching it. A sensitivity analysis is an attempt to identify the parts of the model (i.e. structure, parameter values) that are most important for governing the output. It is an important part of modeling because it is used to quantify the degree of uncertainty in the model prediction and, in many cases, is the main goal of the model (i.e. the model was developed to identify the most important ecological processes). The chapter covers the idea of “local” versus “global” sensitivity analysis via individual parameter perturbation, and how interactive effects of parameters can be revealed via Monte Carlo analysis. Structural versus parameter uncertainty is also explained and explored.

A Design Methodology for Nonlinear Systems Containing Parameter Uncertainty

1984 ◽  
Vol 106 (1) ◽  
pp. 15-20 ◽  
Author(s):  
G. E. Young ◽  
D. M. Auslander
Keyword(s):  
Nonlinear Systems ◽  
Parameter Uncertainty ◽  
Design Methodology ◽  
Search Strategy ◽  
Random Search ◽  
Adjustable Parameter ◽  
Performance Indices ◽  
Adaptive Random Search ◽  
Generalized Sensitivity ◽  
Parameter Values

A design methodology capable of dealing with nonlinear systems containing parameter uncertainty is presented. A generalized sensitivity analysis is incorporated which utilizes sampling of the parameter space and statistical inference. For a system with j adjustable and k nonadjustable parameters, this methodology (which includes an adaptive random search strategy) is used to determine the combination of j adjustable parameter values which maximizes the probability of the performance indices simultaneously satisfying design criteria given the uncertainty in the k nonadjustable parameters.

scholarly journals Empirical Issues in Value-at-Risk

2001 ◽  
Vol 31 (2) ◽  
pp. 299-315 ◽  
Author(s):  
Dennis Bams ◽  
Jacco L. Wielhouwer
Keyword(s):  
At Risk ◽  
Distribution Function ◽  
Parameter Uncertainty ◽  
Value At Risk ◽  
Normal Distribution Function ◽  
Tail Behavior ◽  
Return Distribution ◽  
Relevant Variable ◽  
Var Analysis ◽  
Parameter Values

AbstractFor the purpose of Value-at-Risk (VaR) analysis, a model for the return distribution is important because it describes the potential behavior of a financial security in the future. What is primarily, is the behavior in the tail of the distribution since VaR analysis deals with extreme market situations. We analyze the extension of the normal distribution function to allow for fatter tails and for time-varying volatility. Equally important to the distribution function are the associated parameter values. We argue that parameter uncertainty leads to uncertainty in the reported VaR estimates. There is a tradeoff between more complex tail-behavior and this uncertainty. The “best estimate”-VaR should be adjusted to take account of the uncertainty in the VaR. Finally, we consider the VaR forecast for a portfolio of securities. We propose a method to treat the modeling in a univariate, rather than a multivariate, framework. Such a choice allows us to reduce parameter uncertainty and to model directly the relevant variable.

scholarly journals Multi-parameter uncertainty analysis of a bifurcation point

2006 ◽  
Vol 13 (5) ◽  
pp. 531-540 ◽  
Author(s):  
B. Knopf ◽  
M. Flechsig ◽  
K. Zickfeld
Keyword(s):  
Uncertainty Analysis ◽  
Parameter Space ◽  
Summer Monsoon ◽  
Bifurcation Point ◽  
Parameter Uncertainty ◽  
Climate Models ◽  
Novel Approach ◽  
Wide Range ◽  
Parameter Uncertainty Analysis ◽  
Parameter Values

Abstract. Parameter uncertainty analysis of climate models has become a standard approach for model validation and testing their sensitivity. Here we present a novel approach that allows one to estimate the robustness of a bifurcation point in a multi-parameter space. In this study we investigate a box model of the Indian summer monsoon that exhibits a saddle-node bifurcation against those parameters that govern the heat balance of the system. The bifurcation brings about a change from a wet summer monsoon regime to a regime that is characterised by low precipitation. To analyse the robustness of the bifurcation point itself and its location in parameter space, we perform a multi-parameter uncertainty analysis by applying qualitative, Monte Carlo and deterministic methods that are provided by a multi-run simulation environment. Our results show that the occurrence of the bifurcation point is robust over a wide range of parameter values. The position of the bifurcation, however, is found to be sensitive on these specific parameter choices.

scholarly journals The sensitivity of flowline models of tidewater glaciers to parameter uncertainty

2013 ◽  
Vol 7 (5) ◽  
pp. 1579-1590 ◽  
Author(s):  
E. M. Enderlin ◽  
I. M. Howat ◽  
A. Vieli
Keyword(s):  
Parameter Uncertainty ◽  
Horizontal Resolution ◽  
Model Parameters ◽  
Initial State ◽  
Outlet Glacier ◽  
Tidewater Glaciers ◽  
Flow Models ◽  
Observational Uncertainty ◽  
Physically Based ◽  
Parameter Values

Abstract. Depth-integrated (1-D) flowline models have been widely used to simulate fast-flowing tidewater glaciers and predict change because the continuous grounding line tracking, high horizontal resolution, and physically based calving criterion that are essential to realistic modeling of tidewater glaciers can easily be incorporated into the models while maintaining high computational efficiency. As with all models, the values for parameters describing ice rheology and basal friction must be assumed and/or tuned based on observations. For prognostic studies, these parameters are typically tuned so that the glacier matches observed thickness and speeds at an initial state, to which a perturbation is applied. While it is well know that ice flow models are sensitive to these parameters, the sensitivity of tidewater glacier models has not been systematically investigated. Here we investigate the sensitivity of such flowline models of outlet glacier dynamics to uncertainty in three key parameters that influence a glacier's resistive stress components. We find that, within typical observational uncertainty, similar initial (i.e., steady-state) glacier configurations can be produced with substantially different combinations of parameter values, leading to differing transient responses after a perturbation is applied. In cases where the glacier is initially grounded near flotation across a basal over-deepening, as typically observed for rapidly changing glaciers, these differences can be dramatic owing to the threshold of stability imposed by the flotation criterion. The simulated transient response is particularly sensitive to the parameterization of ice rheology: differences in ice temperature of ~ 2 °C can determine whether the glaciers thin to flotation and retreat unstably or remain grounded on a marine shoal. Due to the highly non-linear dependence of tidewater glaciers on model parameters, we recommend that their predictions are accompanied by sensitivity tests that take parameter uncertainty into account.

scholarly journals The sensitivity of flowline models of tidewater glaciers to parameter uncertainty

2013 ◽  
Vol 7 (3) ◽  
pp. 2567-2593
Author(s):  
E. M. Enderlin ◽  
I. M. Howat ◽  
A. Vieli
Keyword(s):  
Parameter Uncertainty ◽  
Horizontal Resolution ◽  
Model Parameters ◽  
Initial State ◽  
Outlet Glacier ◽  
Tidewater Glaciers ◽  
Flow Models ◽  
Observational Uncertainty ◽  
Physically Based ◽  
Parameter Values

Abstract. Depth-integrated (1-D) flowline models have been widely used to simulate fast-flowing tidewater glaciers and predict future change because their computational efficiency allows for continuous grounding line tracking, high horizontal resolution, and a physically-based calving criterion, which are all essential to realistic modeling of tidewater glaciers. As with all models, the values for parameters describing ice rheology and basal friction must be assumed and/or tuned based on observations. For prognostic studies, these parameters are typically tuned so that the glacier matches observed thickness and speeds at an initial state, to which a perturbation is applied. While it is well know that ice flow models are sensitive to these parameters, the sensitivity of tidewater glacier models has not been systematically investigated. Here we investigate the sensitivity of such flowline models of outlet glacier dynamics to uncertainty in three key parameters that influence a glacier's resistive stress components. We find that, within typical observational uncertainty, similar initial (i.e. steady-state) glacier configurations can be produced with substantially different combinations of parameter values, leading to differing transient responses after a perturbation is applied. In cases where the glacier is initially grounded near flotation across a basal overdeepening, as typically observed for rapidly changing glaciers, these differences can be dramatic owing to the threshold of stability imposed by the flotation criterion. The simulated transient response is particularly sensitive to the parameterization of ice rheology: differences in ice temperature of ∼ 2 °C can determine whether the glaciers thin to flotation and retreat unstably or remain grounded on a marine shoal. Due the highly non-linear dependence of tidewater glaciers on model parameters, we recommend that their predictions are accompanied by sensitivity tests that take parameter uncertainty into account.

scholarly journals A Framework for Automatic Calibration of SWMM Considering Input Uncertainty

2020 ◽  
Author(s):  
Xichao Gao ◽  
Zhiyong Yang ◽  
Dawei Han ◽  
Guoru Huang ◽  
Qian Zhu
Keyword(s):  
Parameter Uncertainty ◽  
Peak Flow ◽  
Storm Water ◽  
Management Model ◽  
Automatic Calibration ◽  
Input Uncertainty ◽  
Storm Water Management Model ◽  
Parameter Estimations ◽  
Parameter Values

Abstract. A new Bayesian framework for automatic calibration of SWMM, which simultaneously considers both parameter uncertainty and input uncertainty, was developed. The framework coupled an optimization algorithm DREAM and the Storm Water Management Model (SWMM) by newly developed API functions used to obtain and adjust parameter values of the model. Besides, a rainfall error model was integrated into the framework to consider systematic rainfall errors. A case study in Guangzhou, China was conducted to demonstrate the use of the framework. The calibration capability of the framework was tested and the impacts of rainfall uncertainty on model parameter estimations and simulated runoff boundaries were identified in the study area. the results show that calibration considering both parameter uncertainty and rainfall uncertainty captures peak flow much better and is more robust in terms of the Nash Sutcliffe index than that only considering parameter uncertainty.

scholarly journals Exploring the Parameters Space of the Regional Climate Model COSMO-CLM 5.0 for the CORDEX Central Asia Domain

2020 ◽  
Author(s):  
Emmanuele Russo ◽  
Silje Lund Sørland ◽  
Ingo Kirchner ◽  
Martijn Schaap ◽  
Christoph C. Raible ◽  
...  
Keyword(s):  
Central Asia ◽  
Parameter Uncertainty ◽  
Climate Models ◽  
Climate Model ◽  
Optimal Parameter ◽  
Regional Climate ◽  
Model Parameters ◽  
Study Results ◽  
Calibration Methods ◽  
Parameter Values

Abstract. The parameter uncertainty of a climate model represents the spectrum of the results obtained by perturbing its empirical and unconfined parameters used to represent sub-grid scale processes. In order to assess a model reliability and to better understand its limitations and sensitivity to different physical processes, the spread of model parameters needs to be carefully investigated. This is particularly true for Regional Climate Models (RCMs), whose performances are domain-dependent. In this study, the parameter space of the RCM COSMO-CLM is investigated for the CORDEX Central Asia domain, using a Perturbed Physics Ensemble (PPE) obtained by performing 1-year long simulations with different parameter values. The main goal is to characterize the parameter uncertainty of the model, and to determine the most sensitive parameters for the region. Moreover, the presented experiments are used to study the effect of several parameters on the simulation of selected variables for sub-regions characterized by different climate conditions, assessing by which degree it is possible to improve model performances by properly selecting parameter inputs in each case. Finally, the paper explores the model parameter sensitivity over different domains, tackling the question of transferability of an RCM model setup to different regions of study. Results show that only a sub-set of model parameters present relevant changes in model performances for different parameter values. Importantly, for almost all parameter inputs, the model shows an opposite behavior among different clusters and regions. This indicates that conducting a calibration of the model against observations to determine optimal parameter values for the Central Asia domain is particularly challenging: in this case, the use of objective calibration methods is highly necessary. Finally, the sensitivity of the model to parameters perturbation for Central Asia is different than the one observed for Europe, suggesting that an RCM should be re-tuned, and its parameter uncertainty properly investigated, when setting up model-experiments to different domains of study.

scholarly journals Exploring the parameter space of the COSMO-CLM v5.0 regional climate model for the Central Asia CORDEX domain

2020 ◽  
Vol 13 (11) ◽  
pp. 5779-5797
Author(s):  
Emmanuele Russo ◽  
Silje Lund Sørland ◽  
Ingo Kirchner ◽  
Martijn Schaap ◽  
Christoph C. Raible ◽  
...  
Keyword(s):  
Central Asia ◽  
Parameter Space ◽  
Parameter Uncertainty ◽  
Climate Model ◽  
Regional Climate ◽  
Model Performance ◽  
Small Scale ◽  
Model Parameters ◽  
Study Results ◽  
Parameter Values

Abstract. The parameter uncertainty of a climate model represents the spectrum of the results obtained by perturbing its empirical and unconfined parameters used to represent subgrid-scale processes. In order to assess a model's reliability and to better understand its limitations and sensitivity to different physical processes, the spread of model parameters needs to be carefully investigated. This is particularly true for regional climate models (RCMs), whose performance is domain dependent. In this study, the parameter space of the Consortium for Small-scale Modeling CLimate Mode (COSMO-CLM) RCM is investigated for the Central Asia Coordinated Regional Climate Downscaling Experiment (CORDEX) domain, using a perturbed physics ensemble (PPE) obtained by performing 1-year simulations with different parameter values. The main goal is to characterize the parameter uncertainty of the model and to determine the most sensitive parameters for the region. Moreover, the presented experiments are used to study the effect of several parameters on the simulation of selected variables for subregions characterized by different climate conditions, assessing by which degree it is possible to improve model performance by properly selecting parameter inputs in each case. Finally, the paper explores the model parameter sensitivity over different domains, tackling the question of transferability of an RCM model setup to different regions of study. Results show that only a subset of model parameters present relevant changes in model performance for different parameter values. Importantly, for almost all parameter inputs, the model shows an opposite behaviour among different clusters and regions. This indicates that conducting a calibration of the model against observations to determine optimal parameter values for the Central Asia domain is particularly challenging: in this case, the use of objective calibration methods is highly necessary. Finally, the sensitivity of the model to parameter perturbation for Central Asia is different than the one observed for Europe, suggesting that an RCM should be retuned, and its parameter uncertainty properly investigated, when setting up model experiments for different domains of study.

Analysis of Myocardial Time-Activity Curves of 123l-Heptadecanoic Acid II. The Acquisition Time

1987 ◽  
Vol 26 (06) ◽  
pp. 248-252 ◽  
Author(s):  
M. J. van Eenige ◽  
F. C. Visser ◽  
A. J. P. Karreman ◽  
C. M. B. Duwel ◽  
G. Westera ◽  
...  
Keyword(s):  
Standard Deviation ◽  
Acquisition Time ◽  
Half Time ◽  
Constant Ratio ◽  
Time Activity ◽  
Time Activity Curve ◽  
Time Value ◽  
Activity Curve ◽  
Low Amplitude ◽  
Parameter Values

Optimal fitting of a myocardial time-activity curve is accomplished with a monoexponential plus a constant, resulting in three parameters: amplitude and half-time of the monoexponential and the constant. The aim of this study was to estimate the precision of the calculated parameters. The variability of the parameter values as a function of the acquisition time was studied in 11 patients with cardiac complaints. Of the three parameters the half-time value varied most strongly with the acquisition time. An acquisition time of 80 min was needed to keep the standard deviation of the half-time value within ±10%. To estimate the standard deviation of the half-time value as a function of the parameter values, of the noise content of the time-activity curve and of the acquisition time, a model experiment was used. In most cases the SD decreased by 50% if the acquisition time was increased from 60 to 90 min. A low amplitude/constant ratio and a high half-time value result in a high SD of the half-time value. Tables are presented to estimate the SD in a particular case.

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