Example Of Sensitivity Analysis Research Articles

Numerical Method for a Risk Model with Two-Sided Jumps and Proportional Investment

In this paper, we consider a risk model with two-sided jumps and proportional investment. The upward jumps and downward jumps represent gains and claims, respectively. Suppose the company invests all of its surplus in a certain proportion in two types of investments, one is risk-free (such as bank accounts) and the other is risky (such as stocks). Our aim is to find the optimal admissible strategy (including the optimal dividend rate and the optimal ratio of investment in risky assets), to maximize the dividend value function, and discuss the effects of a number of parameters on dividend payments. Firstly, the HJB equation of the dividend value function is obtained by the stochastic analysis theory and the dynamic programming method, and the optimal admissible strategy is obtained. Since the integro-differential equation satisfied by the dividend value function is difficult to solve, we turn to the sinc numerical method to approximate solve it. Then, the error between the exact solution (ES) and the sinc approximate solution (SA) is analyzed. Finally, the relative error of a special numerical solution and an ES is given, and some examples of sensitivity analysis are discussed. This study provides a theoretical basis for insurance companies to prevent risks better.

Two-sided jumps risk model with proportional investment and random observation periods

<abstract><p>In this paper, we consider a two-sided jumps risk model with proportional investments and random observation periods. The downward jumps represent the claim while the upward jumps represent the random returns. Suppose an insurance company invests all of their surplus in risk-free and risky investments in proportion. In real life, corporate boards regularly review their accounts rather than continuously monitoring them. Therefore, we assume that insurers regularly observe surplus levels to determine whether they will ruin and that the random observation periods are exponentially distributed. Our goal is to study the Gerber-Shiu function (i.e., the expected discounted penalty function) of the two-sided jumps risk model under random observation. First, we derive the integral differential equations (IDEs) satisfied by the Gerber-Shiu function. Due to the difficulty in obtaining explicit solutions for the IDEs, we utilize the sinc approximation method to obtain the approximate solution. Second, we analyze the error between the approximate and explicit solutions and find the upper bound of the error. Finally, we discuss examples of sensitivity analysis.</p></abstract>

Sensitivity analysis of system reliability using the complex-step derivative approximation

Sensitivity analysis of system failure probability is performed to evaluate the dependence of system reliability on design parameters or component events. Sensitivity analysis is integral for the implementation of efficient gradient-based optimization algorithms in system reliability-based design optimization, and for risk-informed decision-making. This paper presents a method for sensitivity analysis of system failure probability using complex-step differentiation. Many derivative approximations use a small step size to minimize subtractive cancellation errors. The complex-step approximation utilizes an imaginary number, such that the subtractive cancellation is not included in the formulation, resulting in calculations without the associated round-off error. The level of accuracy in sensitivity analysis using the finite difference method (FDM) can vary with change in the step size, which is generally selected arbitrarily, as the actual effect of the step size on the result itself is difficult to predict prior to actual calculation. The complex-step approximation, however, is not confined by the step size, as subtraction cancellation is not included. Compared to the FDM, the complex step approximation has only one limit, the numerical precision of evaluating the function. The proposed method integrates complex-step differentiation into a numerical integration scheme, for the assessment of system reliability and sensitivity. System failure probability and sensitivity are obtained by taking the real and imaginary part of the cumulative distribution function, which is numerically evaluated using the proposed method. The computational efficiency for system reliability problems involving high dimensionality is improved with the utilization of a dimension reduction technique. Numerical examples of sensitivity analysis for series, parallel, and general systems are presented to illustrate the performance of the proposed method.

Systems Biology Approaches to Enzyme Kinetics.

Intracellular drug metabolism involves transport, bioactivation, conjugation, and other biochemical steps. The dynamics of these steps are each dependent on a number of other cellular factors that can ultimately lead to unexpected behavior. In this review, we discuss the confounding processes and coupled reactions within bioactivation networks that require a systems-level perspective in order to fully understand the time-varying behavior. When converting known in vitro characteristics of drug-enzyme interactions into descriptions of cellular systems, features such as substrate availability, cell-to-cell variability, and intracellular redox state, deserve special focus. Two examples are provided. First, a model of hydrogen peroxide clearance during chemotherapy treatment serves as a basis to discuss an example of sensitivity analysis. Second, an example of doxorubicin bioactivation is used for discussing points of consideration when constructing and analyzing network models of drug metabolism.

To what degree does the missing-data technique influence the estimated growth in learning strategies over time? A tutorial example of sensitivity analysis for longitudinal data.

Longitudinal data is almost always burdened with missing data. However, in educational and psychological research, there is a large discrepancy between methodological suggestions and research practice. The former suggests applying sensitivity analysis in order to the robustness of the results in terms of varying assumptions regarding the mechanism generating the missing data. However, in research practice, participants with missing data are usually discarded by relying on listwise deletion. To help bridge the gap between methodological recommendations and applied research in the educational and psychological domain, this study provides a tutorial example of sensitivity analysis for latent growth analysis. The example data concern students’ changes in learning strategies during higher education. One cohort of students in a Belgian university college was asked to complete the Inventory of Learning Styles–Short Version, in three measurement waves. A substantial number of students did not participate on each occasion. Change over time in student learning strategies was assessed using eight missing data techniques, which assume different mechanisms for missingness. The results indicated that, for some learning strategy subscales, growth estimates differed between the models. Guidelines in terms of reporting the results from sensitivity analysis are synthesised and applied to the results from the tutorial example.

Importancia de la caracterización de la biomasa de raíces en la simulación de ecosistemas forestales

Gárate, M., Blanco, J.A. 2013. Importance of root biomass characterization when simulating forest ecosystems. Ecosistemas 22(3):66-73. Doi.: 10.7818/ECOS.2013.22-3.10. Sensitivity analysis are an important tool to understand ecological models functioning, as well as to identify their most important parameters. In addition, sensitivity analysis can be used to design more effective field sampling regimes to calibrate ecological models. When studying forest ecosystems, quantitative analysis of the underground fraction is much more costly and complicated than studying the aboveground fraction, especially when studying the dynamics of production and decomposition of large and fine tree roots. In this work we show an example of sensitivity analysis of the forest ecosystem model FORECAST to parameters defining biomass, longevity and nitrogen concentration in tree roots. The model was calibrated to simulate two Scots pine (Pinus sylvestris L.) stands in the Pyrenees of Navarre. Results indicate that fine root turnover is the most influential parameter on model´s tree growth estimations, followed by fine root N concentration and the root biomass/total tree biomass ratio. Furthermore, the model is more sensitive to root-related parameters when calibrated to simulate poor sites with low productivity capacity and higher nutrient limitation.

PRM159 Sensitivity Analysis Versus Uncertainty Analysis in Health Economic Decision Making

To distinguish sensitivity analysis and uncertainty analysis, characterize their differential roles in health economic decision making, and to provide practical examples of their use and presentation in health economic analysis. The role of one-way sensitivity analysis is to quantify the impact of varying a single parameter on the output of a model. However, this obscures an important distinction between parameter uncertainty and variability. Sensitivity analysis quantifies parameter variability in terms of the percentage change in a model output for a given percentage change in a model input. Sensitivity is therefore an objective property of the model. Uncertainty analysis, on the other hand, propagates a decision maker's subjective parameter uncertainty through a model to estimate the conditional uncertainty of the model output. Accordingly, the functional role of sensitivity analysis is to help a decision maker to understand and validate the internal model structure in order to gain trust in the model itself; whereas the functional role of uncertainty analysis is to assess the potential impact of a decision maker's subjective parameter uncertainty on confidence in a particular model-based decision. These distinctive roles are both critical in health economic analysis and decision making. We provide examples of sensitivity analysis versus uncertainty analysis, show how to report the results of sensitivity and uncertainty analyses, and discuss the implications of this distinction for conducting one-way and probabilistic analyses. Confidence in model-based decision making requires 1) confidence in the model itself, and 2) confidence in the model output given one's subjective parameter uncertainty. Sensitivity analysis and uncertainty analysis, respectively, serve these differential roles.

Mars approach for global sensitivity analysis of differential equation models with applications to dynamics of influenza infection.

Differential equation models are widely used for the study of natural phenomena in many fields. The study usually involves unknown factors such as initial conditions and/or parameters. It is important to investigate the impact of unknown factors (parameters and initial conditions) on model outputs in order to better understand the system the model represents. Apportioning the uncertainty (variation) of output variables of a model according to the input factors is referred to as sensitivity analysis. In this paper, we focus on the global sensitivity analysis of ordinary differential equation (ODE) models over a time period using the multivariate adaptive regression spline (MARS) as a meta model based on the concept of the variance of conditional expectation (VCE). We suggest to evaluate the VCE analytically using the MARS model structure of univariate tensor-product functions which is more computationally efficient. Our simulation studies show that the MARS model approach performs very well and helps to significantly reduce the computational cost. We present an application example of sensitivity analysis of ODE models for influenza infection to further illustrate the usefulness of the proposed method.

Sensitivity Analysis When Data Are Missing Not-at-random

To the Editor: The impact of missing data on the validity of results has often been overlooked in the medical literature.1 Missing data are usually classified as ignorable (including missing completely at random [MCAR] and missing at random [MAR]), and nonignorable (missing not-at-random [MNAR]).2 It is not possible to distinguish between ignorable and nonignorable missing data using observed data. For analysis of ignorable missing data, multiple imputation—a relatively flexible and general purpose approach—is available in standard statistical software,2 and is increasingly used. In contrast, the MNAR hypothesis is rarely explored, although it has been recommended to perform sensitivity analyses through various models for the nonresponse mechanism.2 The mixture modeling principle, which assumes that the variables of interest have different distributions according to the status missing or nonmissing, is an attractive tool.3 The impact of variations in the imputation model on the overall results helps to assess their robustness. One reason for not systematically performing sensitivity analysis could be the lack of simple tools for implementation. We propose a package with an adaptation of the “mice” function from R® software to easily perform sensitivity analysis under various scenarios of nonresponse mechanisms.4,5 The algorithm MICE allows multiple imputation for data sets with mixed types of variables (continuous, binary, categorical). We propose a strategy in 3 steps: Fit an imputation model under the ignorable-missing-data hypothesis by calling the function “mice.” Modify the imputation model by specifying supplementary parameters θ as arguments for the “sens.mice” function. For binary or categorical variables, this parameter is the odds ratio comparing the odds of the modality of interest among subjects with missing value with the odds among subjects without missing value. For continuous variables, this is the difference in expected values. For standardized variables, this difference can be expressed as a coefficient of variation. Impute the missing data using the function sens.mice, resulting in a “mids” object which contains the newly imputed data sets. In the absence of historical data on the missing-data mechanism, we suggest looking for parameter values that modify the overall conclusions, ie, the test results or a point estimate outside of the original confidence interval. These values should be consistent with the targeted exposure effect and should correspond to reasonable hypotheses supported by epidemiologic evidences. As an illustrative example, we apply a sensitivity analysis supposing MNAR data on the data set “CHAIN”6 included in the package “mi.”7 We present results from 4 imputation models that relate poor mental health (as measured by a binary variable) to the self-reported viral load (taken as either a binary or a trinary variable) adjusted on 5 covariates. We assumed that nonresponders were more likely to have high viral load than responders. The magnitude of the variations was in the range of the observed odds ratio between viral load and mental health among complete cases. We compared the results with the complete cases analysis and with the multiple imputation analysis assuming MAR data (Table). The resulting odds ratio was decreased but still substantial. Estimates were robust to the explored MNAR scenarios as conclusions were not modified as compared with multiple imputation; magnitude of the effects was smaller than the assumed variations.TABLE: Example of Sensitivity Analysis on the Odds Ratio Estimating the Association Between Viral Load and Poor Mental Health Using the R Data Set “CHAIN”The “SensMice” package is provided as an eAppendix (https://links.lww.com/EDE/A455). Both the package and the reference manual are freely available at: http://lertim.fr/Members/rgiorgi/DossierPublic/fonctions-r-s/. A sensitivity analysis under different scenarios of nonresponse mechanism could be easily performed using the proposed package. It is of particular interest when the mechanism is highly suspected to be nonignorable, eg, for self-reported characteristics as psychologic disorders, quality of life, or income.8 ACKNOWLEDGMENTS We thank David Hajage and Yann De Rycke for their helpful contributions and Michel Chavance for stimulating discussions. Noémie Resseguier Biostatistics Department Institut Curie Paris, France Roch Giorgi LERTIM, EA 3283 Aix-Marseille University Marseille, France Xavier Paoletti Biostatistics Department Institut Curie Paris, France INSERM U900 Institut Curie Paris, France [email protected]

Design optimization of acoustic radiation from structures under random excitation

Acoustic design optimization of structures subjected to random excitations is investigated in this paper. In this work, a Pseudo excitation method (PEM), an accurate and highly efficient algorithm series for structural stationary random response analysis, is extended to deal with random acoustic radiation problems. A boundary element method (BEM) and a finite element method (FEM) are combined with the PEM to calculate acoustic radiation from random excited structures. A design optimization model is presented, in which the pressure power spectral density (PSD), mass of the structure or eigenvalues of the structure is used as an objective function or constraint function. The thickness of the structure is used as a design variable. Based on acoustic radiation sensitivity analysis and structural sensitivity analysis, the design optimization model is solved with sequential linear programming. Numerical examples of sensitivity analysis and acoustic design optimization are given to demonstrate the effectiveness of the proposed method

Application of a sensitivity equation method to the k–ε model of turbulence

In this paper, we present some examples of sensitivity analysis for flows modeled by the standard k–e model of turbulence with wall functions. The flow and continuous sensitivity equations are solved using an adaptive finite element method. Our examples emphasize a number of applications of sensitivity analysis: identification of the most significant parameters, analysis of the flow model, assessing the influence of closure coefficients, calculation of nearby flows, and uncertainty analysis. The sensitivity parameters considered are closure coefficients of the turbulence model and constants appearing in the wall functions.

Sensitivity analysis in optimal software release time problems

In the modeling of software reliability and in the decision-making using software reliability models, there are a number of parameters whose values are either assumed or estimated based on early data. These parameters are usually inaccurate and thus it is important to study the sensitivity of the estimation. In this paper, the parameter sensitivity problem is studied from two different points of view. First, in addition to point estimation that is commonly used in data analysis, interval estimation is recommended to quantify the errors in the estimated parameters. Second, with the example of sensitivity analysis for the release time determination problem that usually involves both software reliability model parameters and software cost model parameters, a statistical design of experiments technique is employed. This method can not only estimate the effect of separate change of each model parameter, but also estimate the interaction effects when parameters are changed simultaneously. It is useful information for decision maker so that important parameters can be estimated more accurately.

Full-scale modelling of a thermal spray process

An attempt at the comprehensive simulation of a thermal spray process is made. The simulation tool consists of physical models and their computational realisations for major elements of the process such as: plasma torch; particle motion and heating; plasma-substrate and particle-substrate interaction; and formation of the deposited layer. Simulation results are compared with experimental data for LPPS. Using a simplified thermo-mechanical splat model and statistical model of particle deposition, some aspects of microstructure formation are studied. Influence of particle size, temperature and speeds, as well as spray angle and stand-off distance, on the coating structure and surface texture is investigated. Influence of the motion control and process parameters on the coating porosity and microstructure is discussed. Examples of sensitivity analysis and coating optimisation for those parameters are presented.

Dynamic sensitivity analysis and optimum design of aerospace structures

The research and applications of numerical methods of design optimization on structural dynamic behaviors are presented in this paper. The emphasis is focused on the dynamic design optimization of aerospace structures, particularly those composed of composite laminate and sandwich plates. The methods of design modeling, sensitivity analysis on structural dynamic responses, and the optimization solution approaches are presented. The numerical examples of sensitivity analysis and dynamic structural design optimization are given to demonstrate the effectiveness of the numerical methods.

The sensitivity analysis of building thermal network elements

The sensitivity theory was applied with the aim of analyzing the influence of thermal resistance and thermal capacity of construction and the influence of a heat source control factor on unsteady thermal transfer in a building. This paper describes a sensitivity function, sensitivity characteristics and the relationship between sensitivities and tolerances. An example of sensitivity analysis of thermal transfer through the shell of a building is also presented. The method may be used to design building elements for an acceptable indoor environment and low energy consumption.

Shape sensitivity analysis and optimal design of disks and plates with strong discontinuities of kinematic fields

Disks, plates or beams subjected to loading and initial strains or displacements are assumed to be composed of portions interconnected by hinge or slip and dilatancy lines admitting discontinuities in displacements or slopes. The shape of such lines and their stiffness properties are subjected to variation. The sensitivity analysis is first discussed for an arbitrary functional of generalized stress, strain, displacement and boundary traction. The variation of complementary and potential energies is considered as a particular case of a general derivation for sensitivity. The optimal design problem is then considered and the relevant optimally conditions are derived. The general theory is illustrated by examples of sensitivity analysis and optimal design with respect to shape, position and stiffness of discontinuity lines for disks, plates and beams. Numerical aspects of sensitivity analysis are also discussed.

THE STATE OF THE ART OF COSTING HEALTH CARE FOR ECONOMIC EVALUATION

In this paper, the principles of costing health care for economic evaluation are outlined. Hypothetical and published examples are used to illustrate these principles. First, the economic concept of opportunity cost is defined. Secondly, the techniques of economic evaluation which follow from this definition are introduced: they are cost‐benefit analysis, cost‐effectiveness analysis and cost‐utility analysis. Thirdly, a list of costs which should be considered for inclusion in either of these types of evaluation is provided, this listing being based on the concept of opportunity cost. Problems of measurement and valuation of costs are then outlined, focusing in particular on inflation, discounting, marginal costing, patient‐based versus per diem costing, allocating overheads, costing capital and equipment and adjusting distorted market valuations. An example of sensitivity analysis is provided and also a checklist of questions to ask when setting up any costing exercise within an economic evaluation.

A spatial simulation model for vegetation dynamics

A fine-resolution, spatially explicit, stochastic model was developed to simulate the dynamics of species cover abundance and pattern in a single vegetation layer wherein neighbouring individuals are assumed to compete for growing space. Each species in the model is characterized by a small number of morphological and life-history parameters, which enter into equations that stand for a minimal set of vegetation processes. The model performed well in reproducing post-fire successional trends among the three codominant dwarf shrubs in a Dutch heathland community as recorded in an annually mapped permanent quadrat. Program inputs, outputs and an example of sensitivity analysis are illustrated. With suitable changes, the model could potentially describe any plant community in which the vertical structure is simple and community dynamics are determined by spatial interactions among neighbouring plants.

Adjoint network approach to sensitivity calculation for switched‐capacitor networks

AbstractThis paper introduces a computer analytical technique for obtaining the element sensitivities of switched‐capacitor networks (SC networks) with good efficiency by using adjoint networks similar to those for conventional linear networks. The SC networks treated here consist of capacitors, ideal two‐mode switches and operational amplifiers represented by nullator‐norator models. The network equations for the SC networks with amount of charge movement and voltage as variables are so formulated that the network equations of the adjoint networks can be obtained by a simple transformation such as the transpose of their coefficient matrices and with minimum order in many cases. It is also shown that by using Tellegen's theorem in the SC networks, the element sensitivities for capacitors can be obtained as the product of the amount of charge movement in the original SC networks and the voltages in their adjoint networks. Therefore, the element sensitivities can be determined by network analysis of the SC networks and their adjoint networks and the analysis can be performed efficiently with the abovementioned formulation of network equations. Finally, an example of sensitivity analysis by implementing a computer program is shown and its effectiveness is confirmed.

Examining the accuracy of the infinite order sudden approximation using sensitivity analysis

A method is developed for assessing the accuracy of scattering observables calculated within the framework of the infinite order sudden (IOS) approximation. In particular, we focus on the energy sudden assumption of the IOS method and our approach involves the determination of the sensitivity of the IOS scattering matrix SIOS with respect to a parameter which reintroduces the internal energy operator ?0 into the IOS Hamiltonian. This procedure is an example of sensitivity analysis of missing model components (?0 in this case) in the reference Hamiltonian. In contrast to simple first-order perturbation theory a finite result is obtained for the effect of ?0 on SIOS. As an illustration, our method of analysis is applied to integral state-to-state cross sections for the scattering of an atom and rigid rotor. Results are generated within the He+H2 system and a comparison is made between IOS and coupled states cross sections and the corresponding IOS sensitivities. It is found that the sensitivity coefficients are very useful indicators of the accuracy of the IOS results. Finally, further developments and applications are discussed.