Thomas B. Kirchner
- Published in print:
- 2008
- Published Online:
- September 2008
- ISBN:
- 9780195127270
- eISBN:
- 9780199869121
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780195127270.003.0011
- Subject:
- Biology, Ecology, Biochemistry / Molecular Biology
This chapter discusses probabilistic methods for conducting uncertainty analysis, methods that can be use to evaluate both local and global sensitivity of models to parameters, and issues related to ...
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This chapter discusses probabilistic methods for conducting uncertainty analysis, methods that can be use to evaluate both local and global sensitivity of models to parameters, and issues related to the validation of models that express uncertainty in their results. Analytical and Monte Carlo methods for propagating uncertainty through models are described, along with potential limitations of these methods and the problems that can be encountered. The chapter introduces methods for assigning distributions to model parameters. Statistical methods that can be used to help interpret and express the results of probabilistic uncertainty analyses, such as confidence and tolerance intervals, are introduced and their pertinent assumptions are described. Various statistical analyses that can be used for sensitivity analysis and their associated sampling designs are reviewed.Less
This chapter discusses probabilistic methods for conducting uncertainty analysis, methods that can be use to evaluate both local and global sensitivity of models to parameters, and issues related to the validation of models that express uncertainty in their results. Analytical and Monte Carlo methods for propagating uncertainty through models are described, along with potential limitations of these methods and the problems that can be encountered. The chapter introduces methods for assigning distributions to model parameters. Statistical methods that can be used to help interpret and express the results of probabilistic uncertainty analyses, such as confidence and tolerance intervals, are introduced and their pertinent assumptions are described. Various statistical analyses that can be used for sensitivity analysis and their associated sampling designs are reviewed.
E. J. Milner-Gulland and Marcus Rowcliffe
- Published in print:
- 2007
- Published Online:
- January 2008
- ISBN:
- 9780198530367
- eISBN:
- 9780191713095
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198530367.003.0005
- Subject:
- Biology, Biodiversity / Conservation Biology
The effective management of natural resources use requires a mechanistic understanding of the system, not just correlations between variables of the kind discussed in Chapter 4. Understanding may ...
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The effective management of natural resources use requires a mechanistic understanding of the system, not just correlations between variables of the kind discussed in Chapter 4. Understanding may simply be in the form of a conceptual model, but is much more powerful when formalized as a mathematical model. This chapter introduces methods for building a model of the system that can be used to predict future sustainability with or without management interventions. The emphasis is on the simulation of biological and bioeconomic dynamics, for which step-by-step worked examples are given. These examples start with conceptual models, then show how to formalize these as mathematical equations, build these into computer code; test model sensitivity, validity, and alternative structures; and finally, explore future scenarios. Methods for modelling stochasticity and human behaviour are also introduced, as well as the use of Bayesian methods for understanding dynamic systems and exploring management interventions.Less
The effective management of natural resources use requires a mechanistic understanding of the system, not just correlations between variables of the kind discussed in Chapter 4. Understanding may simply be in the form of a conceptual model, but is much more powerful when formalized as a mathematical model. This chapter introduces methods for building a model of the system that can be used to predict future sustainability with or without management interventions. The emphasis is on the simulation of biological and bioeconomic dynamics, for which step-by-step worked examples are given. These examples start with conceptual models, then show how to formalize these as mathematical equations, build these into computer code; test model sensitivity, validity, and alternative structures; and finally, explore future scenarios. Methods for modelling stochasticity and human behaviour are also introduced, as well as the use of Bayesian methods for understanding dynamic systems and exploring management interventions.
Bijan Mohammadi and Olivier Pironneau
- Published in print:
- 2009
- Published Online:
- February 2010
- ISBN:
- 9780199546909
- eISBN:
- 9780191720482
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199546909.003.0008
- Subject:
- Mathematics, Mathematical Physics
This chapter discusses incomplete sensitivity. Incomplete sensitivity means that during sensitivity evaluation, only the deformation of the geometry is accounted for and the change of the state ...
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This chapter discusses incomplete sensitivity. Incomplete sensitivity means that during sensitivity evaluation, only the deformation of the geometry is accounted for and the change of the state variable due to the change of geometry is ignored. The chapter gives the class of functionals for which this assumption can be made. Incomplete sensitivity calculations are illustrated on several model problems, giving the opportunity of introducing low-complexity models for sensitivity analysis. The chapter shows by experience that the accuracy is sufficient for quasi-Newton algorithms, and also that the complexity of the method is drastically reduced making possible real time sensitivity analysis latter used for unsteady applications.Less
This chapter discusses incomplete sensitivity. Incomplete sensitivity means that during sensitivity evaluation, only the deformation of the geometry is accounted for and the change of the state variable due to the change of geometry is ignored. The chapter gives the class of functionals for which this assumption can be made. Incomplete sensitivity calculations are illustrated on several model problems, giving the opportunity of introducing low-complexity models for sensitivity analysis. The chapter shows by experience that the accuracy is sufficient for quasi-Newton algorithms, and also that the complexity of the method is drastically reduced making possible real time sensitivity analysis latter used for unsteady applications.
Diana B. Petitti
- Published in print:
- 1999
- Published Online:
- September 2009
- ISBN:
- 9780195133646
- eISBN:
- 9780199863761
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780195133646.003.15
- Subject:
- Public Health and Epidemiology, Public Health, Epidemiology
Sensitivity analysis is an essential element of decision analysis and cost-effectiveness analysis. This chapter shows how to do sensitivity analysis. It describes one-way, two-way, and three-way ...
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Sensitivity analysis is an essential element of decision analysis and cost-effectiveness analysis. This chapter shows how to do sensitivity analysis. It describes one-way, two-way, and three-way sensitivity analysis and their interpretation with examples. It discusses n-way sensitivity analysis and the application of the principles of sensitivity analysis to systematic reviews with meta-analysis.Less
Sensitivity analysis is an essential element of decision analysis and cost-effectiveness analysis. This chapter shows how to do sensitivity analysis. It describes one-way, two-way, and three-way sensitivity analysis and their interpretation with examples. It discusses n-way sensitivity analysis and the application of the principles of sensitivity analysis to systematic reviews with meta-analysis.
Myoung-Jae Lee
- Published in print:
- 2005
- Published Online:
- February 2006
- ISBN:
- 9780199267699
- eISBN:
- 9780191603044
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/0199267693.003.0006
- Subject:
- Economics and Finance, Econometrics
This chapter continues the discussion of the preceding chapter on how to deal with hidden bias caused by unobserved differences between the treatment (T) and control (C) groups. The preceding chapter ...
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This chapter continues the discussion of the preceding chapter on how to deal with hidden bias caused by unobserved differences between the treatment (T) and control (C) groups. The preceding chapter presented practical and basic approaches; this chapter shows other approaches for hidden bias. Sensitivity analysis examines how a finding obtained under no hidden bias assumption changes as hidden bias is allowed; sensitivity analysis is informative but stops short of giving a definite answer to hidden bias. The more conventional approach would be parametric ‘selection-correction’ or ‘control-function’ methods; these are relatively straightforward to implement, but may be too restrictive. Nonparametric ‘bounding’ approaches would perhaps be too unrestrictive, providing bounds on the treatment effect of interest which are typically too wide to be useful. An approach to avoid hidden bias by controlling for post-treatment covariates is available in some special circumstances.Less
This chapter continues the discussion of the preceding chapter on how to deal with hidden bias caused by unobserved differences between the treatment (T) and control (C) groups. The preceding chapter presented practical and basic approaches; this chapter shows other approaches for hidden bias. Sensitivity analysis examines how a finding obtained under no hidden bias assumption changes as hidden bias is allowed; sensitivity analysis is informative but stops short of giving a definite answer to hidden bias. The more conventional approach would be parametric ‘selection-correction’ or ‘control-function’ methods; these are relatively straightforward to implement, but may be too restrictive. Nonparametric ‘bounding’ approaches would perhaps be too unrestrictive, providing bounds on the treatment effect of interest which are typically too wide to be useful. An approach to avoid hidden bias by controlling for post-treatment covariates is available in some special circumstances.
Julia H. Littell, Jacqueline Corcoran, and Vijayan Pillai
- Published in print:
- 2008
- Published Online:
- January 2009
- ISBN:
- 9780195326543
- eISBN:
- 9780199864959
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780195326543.003.0006
- Subject:
- Social Work, Research and Evaluation
There are several ways to detect publication bias and assess its influence in a meta-analysis. This chapter identifies out-dated methods and describes current approaches. It discusses cumulative ...
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There are several ways to detect publication bias and assess its influence in a meta-analysis. This chapter identifies out-dated methods and describes current approaches. It discusses cumulative meta-analysis and subgroup analysis. Moderator analysis and meta-regression are used to explore variations in effect sizes due to methodological features and other variables in the primary studies. Sensitivity analysis is used to discover the extent to which results of meta-analysis are robust for outliers, and for decisions and assumptions made during the analysis. Finally, statistical power analysis is an important tool for planning and evaluating meta-analyses.Less
There are several ways to detect publication bias and assess its influence in a meta-analysis. This chapter identifies out-dated methods and describes current approaches. It discusses cumulative meta-analysis and subgroup analysis. Moderator analysis and meta-regression are used to explore variations in effect sizes due to methodological features and other variables in the primary studies. Sensitivity analysis is used to discover the extent to which results of meta-analysis are robust for outliers, and for decisions and assumptions made during the analysis. Finally, statistical power analysis is an important tool for planning and evaluating meta-analyses.
Bijan Mohammadi and Olivier Pironneau
- Published in print:
- 2009
- Published Online:
- February 2010
- ISBN:
- 9780199546909
- eISBN:
- 9780191720482
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199546909.003.0005
- Subject:
- Mathematics, Mathematical Physics
This chapter describes sensitivity analysis and automatic differentiation (AD). These include the theory, then an object oriented library for AD by operator overloading, and finally the authors' ...
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This chapter describes sensitivity analysis and automatic differentiation (AD). These include the theory, then an object oriented library for AD by operator overloading, and finally the authors' experience with AD systems using code generation operating in both direct and reverse modes. The chapter describes the different possibilities and through simple programs, gives a comprehensive survey of direct AD by operator overloading and for the reverse mode, the adjoint code method. Several elementary and more advanced examples help the understanding of this central concept.Less
This chapter describes sensitivity analysis and automatic differentiation (AD). These include the theory, then an object oriented library for AD by operator overloading, and finally the authors' experience with AD systems using code generation operating in both direct and reverse modes. The chapter describes the different possibilities and through simple programs, gives a comprehensive survey of direct AD by operator overloading and for the reverse mode, the adjoint code method. Several elementary and more advanced examples help the understanding of this central concept.
Judith Bosmans, Martijn Heymans, Maarten Hupperets, and Maurits van Tulder
- Published in print:
- 2009
- Published Online:
- February 2010
- ISBN:
- 9780199561629
- eISBN:
- 9780191722479
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199561629.003.015
- Subject:
- Public Health and Epidemiology, Public Health, Epidemiology
Next to preventing injuries, it is of increasing interest to have some idea on the cost aspects of injuries and the prevention thereof. What does an injury cost in terms of direct medical costs and ...
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Next to preventing injuries, it is of increasing interest to have some idea on the cost aspects of injuries and the prevention thereof. What does an injury cost in terms of direct medical costs and indirect (e.g. work absenteeism) costs? Additionally, how much can be saved when injuries are prevented, taking into account that preventive measures have certain costs attached as well? This chapter focuses on this relatively new concept for sports injury research and provides background for gathering and analyzing cost data related to sports injury (prevention).Less
Next to preventing injuries, it is of increasing interest to have some idea on the cost aspects of injuries and the prevention thereof. What does an injury cost in terms of direct medical costs and indirect (e.g. work absenteeism) costs? Additionally, how much can be saved when injuries are prevented, taking into account that preventive measures have certain costs attached as well? This chapter focuses on this relatively new concept for sports injury research and provides background for gathering and analyzing cost data related to sports injury (prevention).
Paul Weirich
- Published in print:
- 2004
- Published Online:
- November 2004
- ISBN:
- 9780195171259
- eISBN:
- 9780199834976
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/019517125X.003.0004
- Subject:
- Philosophy, Logic/Philosophy of Mathematics
In some decision problems, even after reflection, relevant probabilities and utilities are indeterminate. Then a rational decision maximizes utility with respect to a quantization of beliefs and ...
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In some decision problems, even after reflection, relevant probabilities and utilities are indeterminate. Then a rational decision maximizes utility with respect to a quantization of beliefs and desires. It is robust with respect to a sensitivity analysis. Rationality does not require meeting the maximin rule, which in its standard form expresses excessive aversion to risk. Multiple decisions must form a coherent set, however.Less
In some decision problems, even after reflection, relevant probabilities and utilities are indeterminate. Then a rational decision maximizes utility with respect to a quantization of beliefs and desires. It is robust with respect to a sensitivity analysis. Rationality does not require meeting the maximin rule, which in its standard form expresses excessive aversion to risk. Multiple decisions must form a coherent set, however.
Andreas C. Arlt, Wolfgang H. Zangemeister, and JÜrgen Dee
- Published in print:
- 1992
- Published Online:
- March 2012
- ISBN:
- 9780195068207
- eISBN:
- 9780199847198
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780195068207.003.0060
- Subject:
- Neuroscience, Sensory and Motor Systems
This paper explains the results of Zangemeister et al. The experimental and modeling results of Hannaford et al. were also reassessed with respect to normally fast and very fast time-optimal ...
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This paper explains the results of Zangemeister et al. The experimental and modeling results of Hannaford et al. were also reassessed with respect to normally fast and very fast time-optimal movements. More importantly, this study employs mathematical and manipulation analysis of the model, specifically the threefold approach of sensitivity analysis to gain valuable insights about the pathologic features of clinical neurologic deficits. The modification of an existing model is also presented and briefly discussed in this chapter. This chapter concludes that applying powerful mathematical tools such as threefold sensitivity analysis to analytic models is helpful in explaining and treating disorders of motor control.Less
This paper explains the results of Zangemeister et al. The experimental and modeling results of Hannaford et al. were also reassessed with respect to normally fast and very fast time-optimal movements. More importantly, this study employs mathematical and manipulation analysis of the model, specifically the threefold approach of sensitivity analysis to gain valuable insights about the pathologic features of clinical neurologic deficits. The modification of an existing model is also presented and briefly discussed in this chapter. This chapter concludes that applying powerful mathematical tools such as threefold sensitivity analysis to analytic models is helpful in explaining and treating disorders of motor control.
Ezra Susser, Sharon Schwartz, Alfredo Morabia, and Evelyn J. Bromet
- Published in print:
- 2006
- Published Online:
- September 2009
- ISBN:
- 9780195101812
- eISBN:
- 9780199864096
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780195101812.003.13
- Subject:
- Public Health and Epidemiology, Public Health, Epidemiology
This chapter provides a framework for the prevention and control of bias due to unequal attrition in cohort studies. Like the effects of third-variable confounding, the effects of unequal attrition ...
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This chapter provides a framework for the prevention and control of bias due to unequal attrition in cohort studies. Like the effects of third-variable confounding, the effects of unequal attrition can be limited by the design, as well as the analysis, of a cohort study. The most problematic kind of attrition is differential. This kind of attrition causes a bias that may not be remediable. The chapter uses sensitivity analysis to gauge the potential bias.Less
This chapter provides a framework for the prevention and control of bias due to unequal attrition in cohort studies. Like the effects of third-variable confounding, the effects of unequal attrition can be limited by the design, as well as the analysis, of a cohort study. The most problematic kind of attrition is differential. This kind of attrition causes a bias that may not be remediable. The chapter uses sensitivity analysis to gauge the potential bias.
Brian P. Ingalls
- Published in print:
- 2009
- Published Online:
- August 2013
- ISBN:
- 9780262013345
- eISBN:
- 9780262258906
- Item type:
- chapter
- Publisher:
- The MIT Press
- DOI:
- 10.7551/mitpress/9780262013345.003.0008
- Subject:
- Biology, Biomathematics / Statistics and Data Analysis / Complexity Studies
This chapter describes the implications of network stoichiometry for sensitivity analysis. It reinterprets the main results of metabolic control analysis (MCA) from the point of view of engineering ...
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This chapter describes the implications of network stoichiometry for sensitivity analysis. It reinterprets the main results of metabolic control analysis (MCA) from the point of view of engineering control theory. The equivalent results are derived from a control-engineering viewpoint, culminating in a control-theoretic interpretation of the main results of metabolic control analysis: the summation and connectivity theorems. It illustrates that MCA offers an extension of standard sensitivity analysis. This chapter bridges the gap between the fields of metabolic control analysis and engineering control theory, further advancing cross-fertilization between these complementary fields.Less
This chapter describes the implications of network stoichiometry for sensitivity analysis. It reinterprets the main results of metabolic control analysis (MCA) from the point of view of engineering control theory. The equivalent results are derived from a control-engineering viewpoint, culminating in a control-theoretic interpretation of the main results of metabolic control analysis: the summation and connectivity theorems. It illustrates that MCA offers an extension of standard sensitivity analysis. This chapter bridges the gap between the fields of metabolic control analysis and engineering control theory, further advancing cross-fertilization between these complementary fields.
Alberto Minujin and Enrique Delamonica
- Published in print:
- 2012
- Published Online:
- September 2012
- ISBN:
- 9781847424822
- eISBN:
- 9781447307235
- Item type:
- chapter
- Publisher:
- Policy Press
- DOI:
- 10.1332/policypress/9781847424822.003.0011
- Subject:
- Sociology, Social Stratification, Inequality, and Mobility
Tanzania has traditionally been an egalitarian society. However, the debt crisis of the 1980s and the ensuing adjustment policies period proved detrimental to equity. The economic recovery recently ...
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Tanzania has traditionally been an egalitarian society. However, the debt crisis of the 1980s and the ensuing adjustment policies period proved detrimental to equity. The economic recovery recently enjoyed by Tanzania has not resulted in a significant reduction of income poverty. While there has been progress in some social indicators it has been unconscionably slow for many dimensions of well-being. These observations call for a deeper analysis of the characteristics of poverty and disparities, moving beyond income poverty and income distribution. Thus, this chapter approaches the issue from the perspective of child poverty and its characteristics. Using a multidimensional approach, the analysis is centered on the depth and severity of child poverty and on the changes between 1999 and 2004/5. The sensitivity analysis indicates the estimation of child poverty is robust to changes in thresholds of various dimensions of deprivation. The analysis of the evidence gives indications on how to pursue effective policies that could improve the situation of children, especially girls, not only in education and nutrition but in the other dimensions as well.Less
Tanzania has traditionally been an egalitarian society. However, the debt crisis of the 1980s and the ensuing adjustment policies period proved detrimental to equity. The economic recovery recently enjoyed by Tanzania has not resulted in a significant reduction of income poverty. While there has been progress in some social indicators it has been unconscionably slow for many dimensions of well-being. These observations call for a deeper analysis of the characteristics of poverty and disparities, moving beyond income poverty and income distribution. Thus, this chapter approaches the issue from the perspective of child poverty and its characteristics. Using a multidimensional approach, the analysis is centered on the depth and severity of child poverty and on the changes between 1999 and 2004/5. The sensitivity analysis indicates the estimation of child poverty is robust to changes in thresholds of various dimensions of deprivation. The analysis of the evidence gives indications on how to pursue effective policies that could improve the situation of children, especially girls, not only in education and nutrition but in the other dimensions as well.
Mark J. Sculpher, Anirban Basu, Karen M. Kuntz, and David O. Meltzer
- Published in print:
- 2016
- Published Online:
- November 2016
- ISBN:
- 9780190492939
- eISBN:
- 9780190492960
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780190492939.003.0011
- Subject:
- Public Health and Epidemiology, Public Health
The key objective of uncertainty analysis is to support better decision making. Uncertainty analysis can help inform the standard decision options of “accept” or “reject,” but extend these options to ...
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The key objective of uncertainty analysis is to support better decision making. Uncertainty analysis can help inform the standard decision options of “accept” or “reject,” but extend these options to include, for example, adoption alongside research or adoption only in the context of research. Since the original Panel’s report, a range of analytical methods has emerged to guide these decisions. We note that deterministic sensitivity analysis can provide useful insights into model behavior and validation, but emphasize that probabilistic sensitivity analysis provides stronger analytical support for decision making. The Second Panel therefore urges that structural uncertainties be tested in analyses, that decision uncertainty be presented using probabilities for specified cost-effectiveness thresholds or cost-effectiveness acceptability curves (CEACs), and that expected value-of-information analysis be used to guide decision making fully by quantifying the value of generating additional evidence.Less
The key objective of uncertainty analysis is to support better decision making. Uncertainty analysis can help inform the standard decision options of “accept” or “reject,” but extend these options to include, for example, adoption alongside research or adoption only in the context of research. Since the original Panel’s report, a range of analytical methods has emerged to guide these decisions. We note that deterministic sensitivity analysis can provide useful insights into model behavior and validation, but emphasize that probabilistic sensitivity analysis provides stronger analytical support for decision making. The Second Panel therefore urges that structural uncertainties be tested in analyses, that decision uncertainty be presented using probabilities for specified cost-effectiveness thresholds or cost-effectiveness acceptability curves (CEACs), and that expected value-of-information analysis be used to guide decision making fully by quantifying the value of generating additional evidence.
Jason E. Shoemaker, Peter S. Chang, Eric C. Kwei, Stephanie R. Taylor, and Francis J. Doyle III
- Published in print:
- 2009
- Published Online:
- August 2013
- ISBN:
- 9780262013345
- eISBN:
- 9780262258906
- Item type:
- chapter
- Publisher:
- The MIT Press
- DOI:
- 10.7551/mitpress/9780262013345.003.0009
- Subject:
- Biology, Biomathematics / Statistics and Data Analysis / Complexity Studies
This chapter introduces the useful model-analytic tools of both sensitivity analysis and structured singular value analysis and their application to cellular networks. It reviews the Nyquist ...
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This chapter introduces the useful model-analytic tools of both sensitivity analysis and structured singular value analysis and their application to cellular networks. It reviews the Nyquist stability criterion and extends it to conditions guaranteeing robust stability (RS). It then examines the structured singular value analysis for robust performance. This chapter shows that control-theoretic tools, such as sensitivity analysis and phase sensitivity, offer powerful means for network elucidation and manipulation in biological systems. It suggests that using tools from control theory to guide both mathematical modeling and experimental design can facilitate the iterative paradigm of systems biology and shed light on the complex network behavior underlying biological organisms.Less
This chapter introduces the useful model-analytic tools of both sensitivity analysis and structured singular value analysis and their application to cellular networks. It reviews the Nyquist stability criterion and extends it to conditions guaranteeing robust stability (RS). It then examines the structured singular value analysis for robust performance. This chapter shows that control-theoretic tools, such as sensitivity analysis and phase sensitivity, offer powerful means for network elucidation and manipulation in biological systems. It suggests that using tools from control theory to guide both mathematical modeling and experimental design can facilitate the iterative paradigm of systems biology and shed light on the complex network behavior underlying biological organisms.
Dale W. Jorgenson, Richard J. Goettle, Mun S. Ho, and Peter J. Wilcoxen
- Published in print:
- 2014
- Published Online:
- September 2014
- ISBN:
- 9780262027090
- eISBN:
- 9780262318563
- Item type:
- chapter
- Publisher:
- The MIT Press
- DOI:
- 10.7551/mitpress/9780262027090.003.0009
- Subject:
- Economics and Finance, Development, Growth, and Environmental
This chapter describes a method for constructing confidence intervals for general equilibrium model results using the covariance matrices routinely computed in the course of estimating the model's ...
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This chapter describes a method for constructing confidence intervals for general equilibrium model results using the covariance matrices routinely computed in the course of estimating the model's parameters. The method is then applied to IGEM to produce confidence intervals for several types of results: (i) the levels of variables in IGEM's base case, (ii) deviations in variables resulting from a policy experiment consisting of a carbon tax used to reduce the rate of tax on capital income, and (iii) the effects of the carbon tax swap on the components of social welfare. For each case, a decomposition analysis is used to identify the key uncertainties underlying the confidence interval. The carbon tax swap is shown to produce statistically significant gains in key variables, including social welfare, along with significant reductions in pollution. The method is also shown to have important advantages over alternative approaches. The confidence intervals it produces are very similar to those generated by Monte Carlo simulation but are much faster to compute for large models. In addition, the decomposition analysis shows that off-diagonal terms in the parameter covariance matrices often contribute significantly to the confidence intervals for key results. By capturing these effects, the method provides better characterization of uncertainty than alternative methodologies that rely on independent perturbations of parameters.Less
This chapter describes a method for constructing confidence intervals for general equilibrium model results using the covariance matrices routinely computed in the course of estimating the model's parameters. The method is then applied to IGEM to produce confidence intervals for several types of results: (i) the levels of variables in IGEM's base case, (ii) deviations in variables resulting from a policy experiment consisting of a carbon tax used to reduce the rate of tax on capital income, and (iii) the effects of the carbon tax swap on the components of social welfare. For each case, a decomposition analysis is used to identify the key uncertainties underlying the confidence interval. The carbon tax swap is shown to produce statistically significant gains in key variables, including social welfare, along with significant reductions in pollution. The method is also shown to have important advantages over alternative approaches. The confidence intervals it produces are very similar to those generated by Monte Carlo simulation but are much faster to compute for large models. In addition, the decomposition analysis shows that off-diagonal terms in the parameter covariance matrices often contribute significantly to the confidence intervals for key results. By capturing these effects, the method provides better characterization of uncertainty than alternative methodologies that rely on independent perturbations of parameters.
Zili Yang
- Published in print:
- 2008
- Published Online:
- August 2013
- ISBN:
- 9780262240543
- eISBN:
- 9780262286510
- Item type:
- chapter
- Publisher:
- The MIT Press
- DOI:
- 10.7551/mitpress/9780262240543.003.0005
- Subject:
- Economics and Finance, Econometrics
This chapter examines the properties of game-theoretic solutions in RICE through sensitivity analysis from an incentive perspective. The issues include intertemporal stability of the grand coalition ...
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This chapter examines the properties of game-theoretic solutions in RICE through sensitivity analysis from an incentive perspective. The issues include intertemporal stability of the grand coalition under the Lindahl social welfare weights, the range of solutions with the core properties or having the Lindahl equilibrium properties, and incentive reactions to false perception of climate change by individual regions.Less
This chapter examines the properties of game-theoretic solutions in RICE through sensitivity analysis from an incentive perspective. The issues include intertemporal stability of the grand coalition under the Lindahl social welfare weights, the range of solutions with the core properties or having the Lindahl equilibrium properties, and incentive reactions to false perception of climate change by individual regions.
Douglas B. Kell and Joshua D. Knowles
- Published in print:
- 2006
- Published Online:
- August 2013
- ISBN:
- 9780262195485
- eISBN:
- 9780262257060
- Item type:
- chapter
- Publisher:
- The MIT Press
- DOI:
- 10.7551/mitpress/9780262195485.003.0001
- Subject:
- Mathematics, Mathematical Biology
This chapter discusses some of the reasons for seeking to model complex cellular biological systems. It begins by presenting a philosophical overview and historical context. It then considers the ...
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This chapter discusses some of the reasons for seeking to model complex cellular biological systems. It begins by presenting a philosophical overview and historical context. It then considers the purposes and implications of modeling; the different kinds of models; and sensitivity analysis.Less
This chapter discusses some of the reasons for seeking to model complex cellular biological systems. It begins by presenting a philosophical overview and historical context. It then considers the purposes and implications of modeling; the different kinds of models; and sensitivity analysis.
Therese M. Donovan and Ruth M. Mickey
- Published in print:
- 2019
- Published Online:
- July 2019
- ISBN:
- 9780198841296
- eISBN:
- 9780191876820
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780198841296.003.0006
- Subject:
- Biology, Biomathematics / Statistics and Data Analysis / Complexity Studies
The “Birthday Problem” expands consideration from two hypotheses to multiple, discrete hypotheses. In this chapter, interest is in determining the posterior probability that a woman named Mary was ...
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The “Birthday Problem” expands consideration from two hypotheses to multiple, discrete hypotheses. In this chapter, interest is in determining the posterior probability that a woman named Mary was born in a given month; there are twelve alternative hypotheses. Furthermore, consideration is given to assigning prior probabilities. The priors represent a priori probabilities that each alternative hypothesis is correct, where a priori means “prior to data collection,” and can be “informative” or “non-informative.” A Bayesian analysis cannot be conducted without using a prior distribution, whether that is an informative prior distribution or a non-informative prior distribution. The chapter discusses objective priors, subjective priors, and prior sensitivity analysis. In addition, the concept of likelihood is explored more deeply.Less
The “Birthday Problem” expands consideration from two hypotheses to multiple, discrete hypotheses. In this chapter, interest is in determining the posterior probability that a woman named Mary was born in a given month; there are twelve alternative hypotheses. Furthermore, consideration is given to assigning prior probabilities. The priors represent a priori probabilities that each alternative hypothesis is correct, where a priori means “prior to data collection,” and can be “informative” or “non-informative.” A Bayesian analysis cannot be conducted without using a prior distribution, whether that is an informative prior distribution or a non-informative prior distribution. The chapter discusses objective priors, subjective priors, and prior sensitivity analysis. In addition, the concept of likelihood is explored more deeply.
I. S. Duff, A. M. Erisman, and J. K. Reid
- Published in print:
- 2017
- Published Online:
- April 2017
- ISBN:
- 9780198508380
- eISBN:
- 9780191746420
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198508380.003.0015
- Subject:
- Mathematics, Numerical Analysis
We consider solving a problem that is closely related to one that we have previously solved or whose parts have previously been solved. We study backward error analysis for sparse problems, obtaining ...
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We consider solving a problem that is closely related to one that we have previously solved or whose parts have previously been solved. We study backward error analysis for sparse problems, obtaining entries of the inverse of a sparse matrix, sparsity in nonlinear problems, solution methods based on orthogonal transformations, and hybrid methods that combine iterative and direct methods.Less
We consider solving a problem that is closely related to one that we have previously solved or whose parts have previously been solved. We study backward error analysis for sparse problems, obtaining entries of the inverse of a sparse matrix, sparsity in nonlinear problems, solution methods based on orthogonal transformations, and hybrid methods that combine iterative and direct methods.
