Sensitivity Analysis For Problems Research Articles

Sensitivity Analysis for Attributable Fraction in the Presence of Unmeasured Confounding.

A main goal of epidemiology is to provide an impact of an exposure on health outcomes. The attributable fraction (AF) is a widely used measure for quantifying its contribution. Various methods have been developed to estimate AF, including standardization, inverse probability of treatment weighting, and doubly robust methods. However, the validity of these methods is established based on the conditional exchangeability assumption, which cannot be tested using only observed data. To assess how vulnerable the research findings are to departures from this assumption, researchers need to conduct a sensitivity analysis. In this study, we propose novel sensitivity analysis methods for AF. Sensitivity analysis problems are formulated as optimization problems, and analytic solutions for the problem are derived. We illustrate our proposed sensitivity analysis methods with a publicly available dataset and examine how the AF of the mother's smoking status during pregnancy for low birth weight changes to the degree of unmeasured confounding.

Sensitivity analysis for unmeasured confounding in estimating the difference in restricted mean survival time.

The difference in restricted mean survival time has been increasingly used as an alternative measure to the hazard ratio in survival analysis. Although some statistical methods have been developed for estimating the difference in restricted mean survival time adjusted for measured confounders in observational studies, the impact of unmeasured confounding on the estimate has rarely been assessed. We develop a novel sensitivity analysis for the estimate of the difference in restricted mean survival time with respect to unmeasured confounding. After formulating the sensitivity analysis problem as an optimization problem, we explain how to obtain the sensitivity range of the difference in restricted mean survival time efficiently and assess its uncertainty using the percentile bootstrap confidence interval. Analytic results are provided for some important survival settings. Simulation studies show that the proposed methods perform well in various settings. We illustrate the proposed sensitivity analysis method by analyzing data from the German Breast Cancer Study Group study.

High sensitivity atomic fluorescence spectroscopy for the detection of AsIII by selective electrolysis of arsenic on nanoflowers-like Fe/NFE

Modified electrosynthetic sample introduction technique is a reliable means of solving the problem of high sensitivity analysis of trace arsenite. This article attempts to achieve selective electroreduction of AsIII through the construction of electrode surfaces with different structures and materials from the perspective of interface reactions. Among the four transition metal modifiers, the iron modified nickel foam electrode with nano-flower structure documented higher efficiency in inducing arsenic reduction and better species selectivity. Systematic electrochemical and spectroscopic tests suggest that strong adsorption effect between Fe and AsIII, appropriate hydrogen evolution potential, and catalytic activity jointly promote efficient electroreduction of AsIII. Optimization based on electrode materials and electrolysis conditions, with high sensitivity, wide linear range (0.1–50 μg L−1), and excellent species selectivity, this paper offers an efficient and economic sample introduction method for trace AsIII/V selective atomic spectroscopy direct determination.

Sensitivity Analysis of Mathematical Models

The construction of a mathematical model of a complicated system is often associated with the evaluation of inputs’ (arguments, factors) influence on the output (response), the identification of important relationships between the variables used, and reduction of the model by decreasing the number of its inputs. These tasks are related to the problems of Sensitivity Analysis of mathematical models. The author proposes an alternative approach based on applying Analysis of Finite Fluctuations that uses the Lagrange mean value theorem to estimate the contribution of changes to the variables of a function to the output change. The article investigates the presented approach on an example of a class of fully connected neural network models. As a result of Sensitivity Analysis, a set of sensitivity measures for each input is obtained. For their averaging, it is proposed to use a point-and-interval estimation algorithm using Tukey’s weighted average. The comparison of the described method with the computation of Sobol’s indices is given; the consistency of the proposed method is shown. The computational robustness of the procedure for finding sensitivity measures of inputs is investigated. Numerical experiments are carried out on the neuraldat data set of the NeuralNetTools library of the R data processing language and on data of the healthcare services provided in the Lipetsk region.

Efficient two-phase approach to reliability-based discrete variable topology optimization of continuum structures with multimodal distributions

In practical applications, some random variables follow multimodal distributions. However, conventional reliability analysis methods in reliability-based topology optimization (RBTO), such as the first order reliability method, often result in considerable computational errors when dealing with problems involving multimodal distributions. Consequently, the corresponding RBTO design is incredible. Moreover, the RBTO problem also faces the challenge of high computational cost. To this end, this paper proposes an efficient two-phase approach for RBTO of continuum structures with multimodal distributions combining sequential approximate integer programming with trust region (SAIP-TR) and direct probability integral method (DPIM). Firstly, DPIM is advanced to address the difficult problems of failure probability estimation and efficient sensitivity analysis under multimodal distributions. Secondly, a reliability-based discrete variable topology optimization framework based on SAIP-TR and DPIM is established, which yields clear topology configurations and facilitates engineering manufacturing. Owing to the merit of SAIP-TR, the original RBTO process is divided into two phases: the first phase performs deterministic topology optimization, and the second phase focuses on RBTO. Moreover, an adaptive selection strategy of representative points, considering structural compliance as performance function, is devised to further enhance computational efficiency. Finally, several examples illustrate high efficiency and accuracy of the proposed approach. The multimodal random variable and the random field are employed separately to describe global and local uncertainties in materials. In contrast, the optimized result considering global material uncertainty is more suitable for additive manufacturing. The proposed approach also presents potential in handling complex RBTO problems with random fields.

Active Kriging-Based Adaptive Importance Sampling for Reliability and燬ensitivity Analyses of Stator Blade Regulator

The reliability and sensitivity analyses of stator blade regulator usually involve complex characteristics like high-nonlinearity, multi-failure regions, and small failure probability, which brings in unacceptable computing efficiency and accuracy of the current analysis methods. In this case, by fitting the implicit limit state function (LSF) with active Kriging (AK) model and reducing candidate sample pool with adaptive importance sampling (AIS), a novel AK-AIS method is proposed. Herein, the AK model and Markov chain Monte Carlo (MCMC) are first established to identify the most probable failure region(s) (MPFRs), and the adaptive kernel density estimation (AKDE) importance sampling function is constructed to select the candidate samples. With the best samples sequentially attained in the reduced candidate samples and employed to update the Kriging-fitted LSF, the failure probability and sensitivity indices are acquired at a lower cost. The proposed method is verified by two multi-failure numerical examples, and then applied to the reliability and sensitivity analyses of a typical stator blade regulator. With methods comparison, the proposed AK-AIS is proven to hold the computing advantages on accuracy and efficiency in complex reliability and sensitivity analysis problems.

A new geometric approach for sensitivity analysis in linear programming

In this paper, we present a new geometric approach for sensitivity analysis in linear programming that is computationally practical for a decision-maker to study the behavior of the optimal solution of the linear programming problem under changes in program data. First, we fix the feasible domain (fix the linear constraints). Then, we geometrically formulate a linear programming problem. Next, we give a new equivalent geometric formulation of the sensitivity analysis problem using notions of affine geometry which consists write the coefficient vector of the objective function in polar coordinate and determining all the angles for which the solution remains unchanged. Finally, the approach is presented in detail and illustrated with a numerical example.

Analysis and classification of privacy-sensitive content in social media posts

User-generated contents often contain private information, even when they are shared publicly on social media and on the web in general. Although many filtering and natural language approaches for automatically detecting obscenities or hate speech have been proposed, determining whether a shared post contains sensitive information is still an open issue. The problem has been addressed by assuming, for instance, that sensitive contents are published anonymously, on anonymous social media platforms or with more restrictive privacy settings, but these assumptions are far from being realistic, since the authors of posts often underestimate or overlook their actual exposure to privacy risks. Hence, in this paper, we address the problem of content sensitivity analysis directly, by presenting and characterizing a new annotated corpus with around ten thousand posts, each one annotated as sensitive or non-sensitive by a pool of experts. We characterize our data with respect to the closely-related problem of self-disclosure, pointing out the main differences between the two tasks. We also present the results of several deep neural network models that outperform previous naive attempts of classifying social media posts according to their sensitivity, and show that state-of-the-art approaches based on anonymity and lexical analysis do not work in realistic application scenarios.

An adaptive method for topology optimization subjected to stationary stochastic forced excitations

Topology optimization subjected to stochastic excitations is usually computationally expensive. This work addresses this challenge by first transforming stochastic response and sensitivity analysis problems at each iteration into a series of frequency response analysis problems, and then an adaptive hybrid expansion method is employed to compute the displacement and adjoint vectors. The proposed method has two features: (1) the derivatives of the eigenpairs are not involved when computing the sensitivities of the responses, thus no special treatment is needed when repeated eigenfrequencies are present; (2) the numbers of lower-order eigenvectors and basis vectors that need to be computed can be determined adaptively according to the given accuracy. The accuracy and efficiency of the proposed method as well as the effect of the excitation frequency on the optimum designs are demonstrated by three numerical examples.

A limited cost consensus approach with fairness concern and its application

People will always consciously or unconsciously compare their cost or benefits of actions with those of others and make judgments about fairness. Aiming at consensus reaching process where decision makers have fairness concern behaviors, this paper proposes a limited cost consensus model with fairness concern. To do this, we define the fairness utility function and fairness utility level based on fairness preference theory and explore some properties. In view of this, we propose a limited cost consensus approach with fairness concern of decision makers, which can obtain a stable and balanced consensus. Through emission reduction consensus problem of Chinese manufacturing enterprises, comparative analysis and sensitivity analysis are used to explain the proposed model. Conclusions about fairness preferences, consensus cost budget, and unit compensation cost can provide significant managerial references for real-world economic and management activities.

Robust One-Class Kernel Spectral Regression.

The kernel null-space technique is known to be an effective one-class classification (OCC) technique. Nevertheless, the applicability of this method is limited due to its susceptibility to possible training data corruption and the inability to rank training observations according to their conformity with the model. This article addresses these shortcomings by regularizing the solution of the null-space kernel Fisher methodology in the context of its regression-based formulation. In this respect, first, the effect of the Tikhonov regularization in the Hilbert space is analyzed, where the one-class learning problem in the presence of contamination in the training set is posed as a sensitivity analysis problem. Next, the effect of the sparsity of the solution is studied. For both alternative regularization schemes, iterative algorithms are proposed which recursively update label confidences. Through extensive experiments, the proposed methodology is found to enhance robustness against contamination in the training set compared with the baseline kernel null-space method, as well as other existing approaches in the OCC paradigm, while providing the functionality to rank training samples effectively.

Debiasing In-Sample Policy Performance for Small-Data, Large-Scale Optimization

Motivated by the poor performance of cross-validation in settings where data are scarce, we propose a novel estimator of the out-of-sample performance of a policy in data-driven optimization. Our approach exploits the optimization problem's sensitivity analysis to estimate the gradient of the optimal objective value with respect to the amount of noise in the data and uses the estimated gradient to debias the policy's in-sample performance. Importantly, unlike cross-validation techniques, our approach avoids sacrificing data for a test set, utilizes all data when training and, hence, is well-suited to settings where data are scarce. We prove bounds on the bias and variance of our estimator for optimization problems with uncertain objectives but known, potentially non-convex, feasible regions. For more specialized optimization problems where the feasible region is ``weakly-coupled in a certain sense, we prove stronger results. Specifically, we provide explicit high-probability bounds on the error of our estimator that holds uniformly over a policy class and depends on the problem's dimension and policy class's complexity. Importantly, all of our bounds show that under mild conditions, the error of our estimator vanishes as the dimension of the optimization problem grows, even if the amount of available data remains small and constant. Said differently, we prove our estimator performs well in the small-data, large-scale regime. Finally, we numerically compare our proposed method to state-of-the-art approaches through a case-study on dispatching emergency medical response services using real data. Our method provides more accurate estimates of out-of-sample performance and learns better-performing policies.

Sensitivity analysis of censoring schemes in progressively type-II right censored order statistics

We study the sensitivity of some optimality criteria based on progressively type-II right censored order statistics scheme changes and explain how the sensitivity analysis helps to find the optimal censoring schemes. We find that determining an optimal censoring plan among a class of one-step censoring schemes is not always recommended. We consider optimality criteria as the model output of a sensitivity analysis problem and quantify how this model depends on its input factor and censoring scheme, using local and global sensitivity methods. Finally, we propose a simple method to find the optimal scheme among all possible censoring schemes.

Reliability sensitivity analysis method based on subset simulation hybrid techniques

• A new sensitivity analysis method based on control variate technique is provided. • A rough failure probability estimator and a correction has been considered. • Subset simulation and importance sampling are employed to reformulate reliability sensitivity analysis. • This method is able to solve reliability sensitivity analysis problems efficiently and accurately. This study proposes a new reliability sensitivity analysis approach using an efficient hybrid simulation method that is a combination of subset simulation, importance sampling and control variates techniques. This method contains a probability term (a fast-moving by subset simulation) and an adaptive weighting part that improves the calculated probability. The Finite Difference Method is used to obtain reliability sensitivities, and the related formulation is derived. Five numerical examples (four-branch model, beam-cable system, one-story frame, ring-stiffened cylinder buckling, and 25-bar steel truss) are presented to describe the applications of the proposed method. The results are compared with those obtained by the available techniques. The results revealed that the proposed method efficiently and accurately solves rare-event, system-level, and real-world engineering problems with explicit and implicit limit state functions.

Robust sensitivity analysis for linear programming with ellipsoidal perturbation

Sensitivity analysis is applied to the robust linear programming problem in this paper. The coefficients of the linear program are assumed to be perturbed in three perturbation manners within ellipsoidal sets. Our robust sensitivity analysis is to calculate the maximal radii of the perturbation sets to keep some properties of the robust feasible set. Mathematical models are formulated for the robust sensitivity analysis problems and all models are either reformulated into linear programs or convex quadratic programs except for the bi-convex programs where more than one row of the constraint matrix is perturbed. For the bi-convex programs, we develop a binary search algorithm.

Alternative Adjoint Boltzmann Transport Operators in Alternative Hilbert Spaces in Spherical Geometry: Theory and Paradigm Applications

The solution of the customary adjoint Boltzmann equation for linear transport of particles and radiation, referred to as the “adjoint flux,” plays a prominent role in reactor physics, shielding, control, and optimization as a weighting function for cross-section processing, optimization, Monte Carlo acceleration procedures, and sensitivity and uncertainty analyses. All of the textbooks and scientific works published thus far use the same procedure to derive “the” adjoint Boltzmann operator, thereby conveying inadvertently the misleading impression that this traditional procedure is the only way to obtain “the” adjoint Boltzmann operator, and that the form of “the” adjoint operator thus derived is universally unique. None of the works published in the literature thus far touches on the fact that the customary textbook-form of the adjoint Boltzmann operator is actually derived in a particular Hilbert space, which is endowed with a specific inner product that is based on integrating spatially over the domain’s spatial volume such that Gauss’ divergence theorem holds. As this work will show, however, the Hilbert space that has been implicitly used in all of the published works thus far is not the only possible Hilbert space for deriving operators that are adjoint, in the respective Hilbert space, to the forward Boltzmann operator. Alternative Hilbert spaces may be used just as legitimately, and may actually be more suitable than the customary Hilbert space for computing adjoint functions to be used in inner products involving various forward and/or adjoint fluxes and forward and/or adjoint source terms.By presenting paradigm illustrative examples in three-dimensional spherical coordinates, this work shows that although a unique form of the adjoint Boltzmann operator is obtained for each Hilbert space in which the respective adjoint operator is constructed, distinct Hilbert spaces will produce distinct adjoint Boltzmann operators accompanied by distinct forms of the corresponding bilinear concomitants on the respective spatial domain’s boundary. The fundamental practical reason for using alternative Hilbert spaces is to obtain alternative adjoint functions and/or Green’s functions that may be less singular than the customary adjoint function and/or Green’s functions (in the customary Hilbert space) and would consequently be computable numerically. As this work shows, such situations arise when attempting to use the adjoint sensitivity analysis methodology in the conventional Hilbert space for computing sensitivities to cross sections, isotopic number densities, etc., of responses of flux and/or power detectors placed near or at the center of the spherical coordinates. In such sensitivity analysis problems, the singularities of the conventional adjoint Boltzmann equation in the conventional Hilbert space may preclude its use, but the requisite sensitivities can nevertheless be computed efficiently using an alternative adjoint Boltzmann equation in an alternative Hilbert space. The consequences of this powerful breakthrough new concept of using alternative adjoint operators in alternative Hilbert spaces are highlighted by presenting a paradigm benchmark problem that admits a closed-form exact solution. This benchmark problem shows that the customary adjoint equation becomes singular at the sphere’s center, so the conventional adjoint flux is therefore noncomputable there, but the alternative adjoint transport equation in a judiciously chosen alternative Hilbert space is everywhere nonsingular and can therefore be used to compute the requisite sensitivities. By indicating the path for using alternative Hilbert spaces, this work opens new conceptual procedures for solving problems that have hitherto been unsolvable in the framework of the conventional adjoint particle transport equation.

Kriging-sparse Polynomial Dimensional Decomposition surrogate model with adaptive refinement

Uncertainty Quantification and Sensitivity Analysis problems are made more difficult in the case of applications involving expensive computer simulations. This is because a limited amount of simulations is available to build a sufficiently accurate metamodel of the quantities of interest.In this work, an algorithm for the construction of a low-cost and accurate metamodel is proposed, having in mind computationally expensive applications. It has two main features. First, Universal Kriging is coupled with sparse Polynomial Dimensional Decomposition (PDD) to build a metamodel with improved accuracy. The polynomials selected by the adaptive PDD representation are used as a sparse basis to build a Universal Kriging surrogate model. Secondly, a numerical method, derived from anisotropic mesh adaptation, is formulated in order to adaptively insert a fixed number of new training points to an existing Design of Experiments.The convergence of the proposed algorithm is analyzed and assessed on different test functions with an increasing size of the input space. Finally, the algorithm is used to propagate uncertainties in two high-dimensional real problems related to the atmospheric reentry.

Revisiting the Basis of Sensitivity Analysis for Dynamical Earth System Models

AbstractThis paper investigates the problem of global sensitivity analysis (GSA) of Dynamical Earth System Models and proposes a basis for how such analyses should be performed. We argue that (a) performance metric‐based approaches to parameter GSA are actually identifiability analyses, (b) the use of a performance metric to assess sensitivity unavoidably distorts the information provided by the model about relative parameter importance, and (c) it is a serious conceptual flaw to interpret the results of such an analysis as being consistent and accurate indications of the sensitivity of the model response to parameter perturbations. Further, because such approaches depend on availability of system state/output observational data, the analysis they provide is necessarily incomplete. Here we frame the GSA problem from first principles, using trajectories of the partial derivatives of model outputs with respect to controlling factors as the theoretical basis for sensitivity, and construct a global sensitivity matrix from which statistical indices of total period time‐aggregateparameter importance, and time series of time‐varying parameter importance, can be inferred. We demonstrate this framework using theHBV‐SASKconceptual hydrologic model applied to the Oldman basin in Canada and show that it disagrees with performance metric‐based methods regarding which parameters exert the strongest controls on model behavior. Further, it is highly efficient, requiring less than 1,000 base samples to obtain stable and robust parameter importance assessments for our 10‐parameter example.

Geometric Sensitivity Measures for Bayesian Nonparametric Density Estimation Models

We propose a geometric framework to assess global sensitivity in Bayesian nonparametric models for density estimation. We study sensitivity of nonparametric Bayesian models for density estimation, based on Dirichlet-type priors, to perturbations of either the precision parameter or the base probability measure. To quantify the different effects of the perturbations of the parameters and hyperparameters in these models on the posterior, we define three geometrically-motivated global sensitivity measures based on geodesic paths and distances computed under the nonparametric Fisher-Rao Riemannian metric on the space of densities, applied to posterior samples of densities: (1) the Fisher-Rao distance between density averages of posterior samples, (2) the log-ratio of Karcher variances of posterior samples, and (3) the norm of the difference of scaled cumulative eigenvalues of empirical covariance operators obtained from posterior samples. We validate our approach using multiple simulation studies, and consider the problem of sensitivity analysis for Bayesian density estimation models in the context of three real datasets that have previously been studied.

Thermodynamic modeling and sensitivity analysis of ejector in refrigeration system

This paper focuses on the problems of thermodynamic modeling and sensitivity analysis of the ejector in refrigeration. Firstly, a new thermodynamic model is proposed based on the assumptions of constant pressure mixing and constant area mixing. The proposed model contains fewer parameters and simpler structure compared with the traditional ejector models. Later, the sensitivity analysis of the ejector is carried out based on the adjoint sensitivity method. Three different sensitivity coefficients are given to reveal the relation between design parameters and ejector performance. The result shows that geometric parameters have the most influences on the entrainment ratio of the ejector. For the ejector using R600a, the sensitivity coefficients of entrainment ratio to At and Am are -2.43% and 2.40% respectively.