Global Sensitivity Analysis Techniques Research Articles

Calibration of LEACHN model using LH-OAT sensitivity analysis

LEACHN model is useful to describe the nitrogen transport and transformation in soil but requires many input parameters. A sensitivity analysis can help to sort out the sensitive ones among many input parameters. A global sensitivity analysis technique, Latin Hypercube One factor At a Time (LH-OAT) method, was applied to LEACHN model in this study. Only a few parameters were found to be sensitive compared to many input parameters of the model from the sensitivity analysis. Using the results from the sensitivity analysis, calibration and validation of LEACHN model for nitrate leaching was performed for the experimental results from pot experiments that consisted of six types with different soil depth in mini-lysimeters and different fertilizer additions. The results indicated that the use of LH-OAT method could help the facile field application of LEACHN model. Model fitting could be improved by adopting current values in yearly crop parameters in validation.

Global Sensitivity Analysis Techniques for Probabilistic Ground Water Modeling

Global sensitivity analysis techniques are better suited for analyzing input-output relationships over the full range of parameter variations and model outcomes, as opposed to local sensitivity analysis carried out around a reference point. This article describes three such techniques: (1) stepwise rank regression analysis for building input-output models to identify key contributors to output variance, (2) mutual information (entropy) analysis for determining the strength of nonmonotonic patterns of input-output association, and (3) classification tree analysis for determining what variables or combinations are responsible for driving model output into extreme categories. These techniques are best applied in conjunction with Monte Carlo simulation-based probabilistic analyses. Two examples are presented to demonstrate the applicability of these methods. The usefulness of global sensitivity techniques is examined vis-a-vis local sensitivity analysis methods, and recommendations are provided for their applications in ground water modeling practice.

Global Sensitivity Analysis for the determination of parameter importance in bio‐manufacturing processes

The present paper describes the application of GSA (Global Sensitivity Analysis) techniques to mathematical models of bioprocesses in order to rank inputs such as feed titres, flow rates and matrix capacities for the relative influence that each exerts upon outputs such as yield or throughput. GSA enables quantification of both the impact of individual variables on process outputs, as well as their interactions. These data highlight those attributes of a bioprocess which offer the greatest potential for achieving manufacturing improvements. Whereas previous GSA studies have been limited to individual unit operations, this paper extends the treatment to an entire downstream process and illustrates its utility by application to the production of a Fab-based rattlesnake antivenom called CroFab [(Crotalidae Polyvalent Immune Fab (Ovine); Protherics U.K. Limited]. Initially, hyperimmunized ovine serum containing rattlesnake antivenom IgG (product), other antibodies and albumin is applied to a synthetic affinity ligand adsorbent column to separate the antibodies from the albumin. The antibodies are papain-digested into Fab and Fc fragments, before concentration by ultrafiltration. Fc, residual IgG and albumin are eliminated by an ion-exchanger and then CroFab-specific affinity chromatography is used to produce purified antivenom. Application of GSA to the model of this process showed that product yield was controlled by IgG feed concentration and the synthetic-material affinity column's capacity and flow rate, whereas product throughput was predominantly influenced by the synthetic material's capacity, the ultrafiltration concentration factor and the CroFab affinity flow rate. Such information provides a rational basis for identifying the most promising strategies for delivering improvements to commercial-scale biomanufacturing processes.

Sensitivity analysis and robust experimental design of a signal transduction pathway system

AbstractExperimental design for cellular networks based on sensitivity analysis is studied in this work. Both optimal and robust experimental design strategies are developed for the IκB‐NF‐κB signal transduction model. Based on local sensitivity analysis, the initial IKK intensity is calculated using an optimal experimental design process, and several scalarization measures of the Fisher information matrix are compared. Global sensitivity analysis and robust experimental design techniques are then developed to consider parametric uncertainties in the model. The modified Morris method is employed in global sensitivity analysis, and a semidefinite programming method is exploited to implement the robust experimental design for the problem of measurement set selection. The parametric impacts on the oscillatory behavior of NF‐κB in the nucleus are also discussed. © 2008 Wiley Periodicals, Inc. Int J Chem Kinet 40: 730–741, 2008

Quantifying heterogeneity in exposure–risk relationships using exhaled breath biomarkers for 1,3-butadiene exposures

The health effects of human exposure to 1,3-butadiene (BD) have been extensively studied using both epidemiological and animal toxicology approaches. However, various data and knowledge gaps remain, one of which is an understanding of the human heterogeneity in BD dosimetry. The objective of our study was to better understand the role of individual variability in delivered tissue dose. We designed a study of laboratory exposures of a relatively large group of healthy human subjects. Subjects were then exposed to 2.0 ppm BD through a face mask for 20 min, followed by 40 min of breathing clean air. Exhaled breath concentrations of BD were measured at ten time points during and after exposure, and a three-compartment physiologically based pharmacokinetic (PBPK) model was used to quantify the kinetic behavior of BD. We implemented a Markov chain Monte Carlo procedure to fit the model to the experimental data, and used global sensitivity analysis techniques to examine the sensitivity of exhaled breath concentrations to PBPK model parameters. Uptake during exposure was strongly influenced by rebreathing of exhaled BD during exposure; inclusion of rebreathing in the model simulations resulted in a 21% increase in the amount of BD retained in the body. We found that uptake ranged from 38% to 77% across individuals. We measured considerable intra-individual variability from 11 subjects who underwent the testing twice. Most of this variation stemmed from phase I metabolism of BD, which varied by as much as a factor of 2.6 within individuals. Overall, we have sought to quantify the sources of inter- and intra-individual variabilities in the pharmacokinetic behavior of BD. The results of our research may impact the current framework for biomarker and pharmacokinetic studies by improving our understanding of the sources of heterogeneity in response to chemical exposures.

Calculating first-order sensitivity measures: A benchmark of some recent methodologies

This work compares three different global sensitivity analysis techniques, namely the state-dependent parameter (SDP) modelling, the random balance designs, and the improved formulas of the Sobol’ sensitivity indices. These techniques are not yet commonly known in the literature. Strengths and weaknesses of each technique in terms of efficiency and computational cost are highlighted, thus enabling the user to choose the more suitable method depending on the computational model analysed. Two test functions proposed in the literature are considered. Computational costs and convergence rates for each function are compared and discussed.

Modeling study on aerosol dynamical processes regulating new particle and CCN formation at clean continental areas

The formation of new particles and CCNs under conditions typical for clean continental areas has been investigated by performing simulations with an aerosol dynamical model. The main goal was to quantify the relative importance of the key dynamic parameters to new‐particle and CCN formation. To this end, the model output was analyzed using a global sensitivity analysis technique. It was shown that there is no unambiguous answer to the question regarding the most important factor regulating new particle formation (NPF). Instead, the answer depends largely on the relative magnitudes of the pre‐existing particle surface area and emission rates of aerosol precursors which vary according to the atmospheric conditions. We also demonstrate that different factors may control the formation of particles with detectable sizes and particles having larger, climatically relevant sizes. These results suggest that varying, problem‐specific approaches should be adopted in large scale modeling of NPF.

From local to global importance measures of uncertainty propagation in composite structures

Abstract The influence of uncertainties of input parameters on output response of composite structures is investigated in this paper. In particular, the effects of deviations in mechanical properties, ply angles, ply thickness and on applied loads are studied. The uncertainty propagation and the importance measure of input parameters are analysed using three different approaches: a first-order local method, a Global Sensitivity Analysis (GSA) supported by a variance-based method and an extension of local variance to estimate the global variance over the domain of inputs. Sample results are shown for a shell composite laminated structure built with different composite systems including multi-materials. The importance measures of input parameters on structural response based on numerical results are established and discussed as a function of the anisotropy of composite materials. Needs for global variance methods are discussed by comparing the results obtained from different proposed methodologies. The objective of this paper is to contribute for the use of GSA techniques together with low expensive local importance measures.

Analysing DSGE Models with Global Sensitivity Analysis

We present computational tools to analyse some key properties of DSGE models and address the following questions: (i) Which is the domain of structural coefficients assuring the stability and determinacy of a DSGE model? (ii) Which parameters mostly drive the fit of, e.g., GDP and which the fit of inflation? Is there any conflict between the optimal fit of one observed series versus another one? (iii) How to represent in a direct, albeit approximated, form the relationship between structural parameters and the reduced form of a rational expectations model? Global sensitivity analysis (GSA) techniques are used to answer these questions. We will discuss two classes of methods: Monte Carlo filtering (MCF) techniques and functional/variance decomposition techniques. These tools can make the model properties more transparent; helping the analyst to identify critical elements in the specification and, if necessary, guiding her to revise the model; supporting calibration and estimation procedures and interpreting estimation results. Applications to small DSGE models will complete the description of the methodologies.

A general first-order global sensitivity analysis method

Fourier amplitude sensitivity test (FAST) is one of the most popular global sensitivity analysis techniques. The main mechanism of FAST is to assign each parameter with a characteristic frequency through a search function. Then, for a specific parameter, the variance contribution can be singled out of the model output by the characteristic frequency. Although FAST has been widely applied, there are two limitations: (1) the aliasing effect among parameters by using integer characteristic frequencies and (2) the suitability for only models with independent parameters. In this paper, we synthesize the improvement to overcome the aliasing effect limitation [Tarantola S, Gatelli D, Mara TA. Random balance designs for the estimation of first order global sensitivity indices. Reliab Eng Syst Safety 2006; 91(6):717–27] and the improvement to overcome the independence limitation [Xu C, Gertner G. Extending a global sensitivity analysis technique to models with correlated parameters. Comput Stat Data Anal 2007, accepted for publication]. In this way, FAST can be a general first-order global sensitivity analysis method for linear/nonlinear models with as many correlated/uncorrelated parameters as the user specifies. We apply the general FAST to four test cases with correlated parameters. The results show that the sensitivity indices derived by the general FAST are in good agreement with the sensitivity indices derived by the correlation ratio method, which is a non-parametric method for models with correlated parameters.

Extending a global sensitivity analysis technique to models with correlated parameters

The identification and representation of uncertainty is recognized as an essential component in model applications. One important approach in the identification of uncertainty is sensitivity analysis. Sensitivity analysis evaluates how the variations in the model output can be apportioned to variations in model parameters. One of the most popular sensitivity analysis techniques is Fourier amplitude sensitivity test (FAST). The main mechanism of FAST is to assign each parameter with a distinct integer frequency (characteristic frequency) through a periodic sampling function. Then, for a specific parameter, the variance contribution can be singled out of the model output by the characteristic frequency based on a Fourier transformation. One limitation of FAST is that it can only be applied for models with independent parameters. However, in many cases, the parameters are correlated with one another. In this study, we propose to extend FAST to models with correlated parameters. The extension is based on the reordering of the independent sample in the traditional FAST. We apply the improved FAST to linear, nonlinear, nonmonotonic and real application models. The results show that the sensitivity indices derived by FAST are in a good agreement with those from the correlation ratio sensitivity method, which is a nonparametric method for models with correlated parameters.

SENSITIVITY ANALYSIS OF APEX FOR NATIONAL ASSESSMENT

Sensitivity analysis for mathematical simulation models is helpful in identifying influential parameters for modeloutputs. Representative sets of APEX (Agricultural Policy/Environmental eXtender) model data from across the U.S. wereused for sensitivity analysis to identify influential parameters for APEX outputs of crop grain yields, runoff/water yield, waterand wind erosion, nutrient loss, and soil carbon change for a national assessment project: the Conservation EffectsAssessment Project (CEAP). The analysis was based on global sensitivity analysis techniques. A test case, randomly selectedfrom the representative sets of APEX model data, was first analyzed using both the variance-based sensitivity analysistechnique and the enhanced Morris method. The analysis confirmed the reliability of the enhanced Morris measure inscreening subsets of influential and non-influential parameters. Therefore, the enhanced Morris method was used for thenational assessment, where the cost of applying variance-based techniques would be excessive. Although sensitivities aredynamic in both temporal and spatial dimensions, the very influential parameters (ranking 1st and 2nd) appear veryinfluential in most cases. Statistical analyses identified that the NRCS curve number index coefficient is very influential forrunoff and water-related output variables, such as soil loss by water, N and P losses in runoff. The Hargreaves PET equationexponent, moisture fraction required for seed germination, RUSLE C factor coefficient, and the potential heat units areinfluential for more than two APEX outputs studied.

Uncertainty and global sensitivity analysis in the evaluation of investment projects

This paper discusses the use of global sensitivity analysis (SA) techniques in investment decisions. Global SA complements and improves uncertainty analysis (UA) providing the analyst/decision- maker with information on how uncertainty is apportioned by the uncertain factors. In this work, we introduce global SA in the investment project evaluation realm. We then need to deal with two aspects: (1) the identification of the appropriate global SA method to be used and (2) the interpretation of the results from the decision maker point of view. For task 1, we compare the performance of two family of techniques: non-parametric and variance decomposition based. For task 2, we explore the determination of the cash flow global importance (GI) for valuation criteria utilized in investment project evaluation. For the net present value (NPV), we show that it is possible to derive an analytical expression of the cash flow GI, which is the same for all the techniques. This knowledge enables us to: (1) offer a direct way to compute cash flow GI; (2) illustrate the practical impact of global SA on the information collection process. For the internal rate of return (IRR), we show that the same conclusions cannot be driven. In particular, (a) one has to utilize a numerical approach for the computation of the cash flow influence, since an analytical expression cannot be found and (b) different techniques can produce different ranking. These observations are illustrated by means of the application to a model utilized in the energy sector for the evaluation of projects under survival risk. The quantitative comparison of cash flow ranking with respect to the NPV and IRR concludes the paper, illustrating that information obtained from the SA of the NPV cannot be transferred to the IRR.

A comparison between the uncertainties in model parameters and in forcing functions: its application to a 3D water-quality model

This paper illustrates the application of both local and global sensitivity analysis techniques to an estimation of the uncertainty in the output of a 3D reaction–diffusion ecological model; the model describes the seasonal dynamics of dissolved Nitrogen and Phosphorous, and those of the phytoplanktonic and zooplanktonic communities in the lagoon of Venice. Two sources of uncertainty were taken into account and compared: (1) uncertainty concerning the parameters of the governing equation; (2) uncertainty concerning the forcing functions. The mean annual concentrations of Dissolved Inorganic Nitrogen (DIN) was regarded as the model output, as it represents the largest fraction of the Total Dissolved Nitrogen, TDN, for which the current Italian legislation sets a quality target in the lagoon of Venice. A local sensitivity analysis was initially used, so as to rank the parameters and provide an initial estimation of the uncertainty, which is a result of an imperfect knowledge of the dynamic of the system. This uncertainty was compared with that induced by an imperfect knowledge of the loads of Nitrogen, which represent the main forcing functions. On the basis of the results of the local analysis, the most important parameters and loads were then taken as the sources of uncertainty, in an attempt to assess their relative contributions. The global uncertainty and sensitivity analyses were carried out by means of a sampling-based Monte Carlo method. The results of the subsequent input–output regression analysis suggest that the variance in the model output could be partitioned among the sources of uncertainty, in accordance with a linear model. Based on this model, 79% of the variance in the mean annual concentration of DIN was accounted for by the uncertainty in the parameters which specify the dynamics of the phytoplankton and zooplankton, and only 5% by the uncertainties in the three main Nitrogen sources.

Optimizing Genetic Circuits by Global Sensitivity Analysis

Artificial genetic circuits are becoming important tools for controlling cellular behavior and studying molecular biosystems. To genetically optimize the properties of complex circuits in a practically feasible fashion, it is necessary to identify the best genes and/or their regulatory components as mutation targets to avoid the mutation experiments being wasted on ineffective regions, but this goal is generally not achievable by current methods. The Random Sampling—High Dimensional Model Representation (RS-HDMR) algorithm is employed in this work as a global sensitivity analysis technique to estimate the sensitivities of the circuit properties with respect to the circuit model parameters, such as rate constants, without knowing the precise parameter values. The sensitivity information can then guide the selection of the optimal mutation targets and thereby reduce the laboratory effort. As a proof of principle, the in vivo effects of 16 pairwise mutations on the properties of a genetic inverter were compared against the RS-HDMR predictions, and the algorithm not only showed good consistency with laboratory results but also revealed useful information, such as different optimal mutation targets for optimizing different circuit properties, not available from previous experiments and modeling.

Comparison of global sensitivity analysis techniques and importance measures in PSA : Borgonovo, E. et al. Reliability Engineering & System Safety, 2003, 79, (2), 175–185

Comparison of global sensitivity analysis techniques and importance measures in PSA : Borgonovo, E. et al. Reliability Engineering & System Safety, 2003, 79, (2), 175–185

Comparison of global sensitivity analysis techniques and importance measures in PSA

This paper discusses application and results of global sensitivity analysis techniques to probabilistic safety assessment (PSA) models, and their comparison to importance measures. This comparison allows one to understand whether PSA elements that are important to the risk, as revealed by importance measures, are also important contributors to the model uncertainty, as revealed by global sensitivity analysis. We show that, due to epistemic dependence, uncertainty and global sensitivity analysis of PSA models must be performed at the parameter level. A difficulty arises, since standard codes produce the calculations at the basic event level. We discuss both the indirect comparison through importance measures computed for basic events, and the direct comparison performed using the differential importance measure and the Fussell ‐ Vesely importance at the parameter level. Results are discussed for the large LLOCA sequence of the advanced test reactor PSA. q 2002 Elsevier Science Ltd. All rights reserved.