@article{Jansen1999,
abstract = {A scalar model output Y is assumed to depend deterministically on a set of stochastically independent input vectors of different dimensions. The composition of the variance of Y is considered; variance components of particular relevance for uncertainty analysis are identified. Several analysis of variance designs for estimation of these variance components are discussed. Classical normal-model theory can suggest optimal designs. The designs can be implemented with various sampling methods: ordinary random sampling, latin hypercube sampling and scrambled quasi-random sampling. Some combinations of design and sampling method are compared in two small-scale numerical experiments.},
author = {Jansen, M.},
doi = {10.1016/S0010-4655(98)00154-4},
journal = {Computer Physics Communications},
number = {1},
pages = {35--43},
title = {{Analysis of variance designs for model output}},
volume = {117},
year = {1999}
}
@article{Saltelli2010a,
abstract = {Variance based methods have assessed themselves as versatile and effective among the various available techniques for sensitivity analysis of model output. Practitioners can in principle describe the sensitivity pattern of a model Y = f (X1, X2, ..., Xk) with k uncertain input factors via a full decomposition of the variance V of Y into terms depending on the factors and their interactions. More often practitioners are satisfied with computing just k first order effects and k total effects, the latter describing synthetically interactions among input factors. In sensitivity analysis a key concern is the computational cost of the analysis, defined in terms of number of evaluations of f (X1, X2, ..., Xk) needed to complete the analysis, as f (X1, X2, ..., Xk) is often in the form of a numerical model which may take long processing time. While the computational cost is relatively cheap and weakly dependent on k for estimating first order effects, it remains expensive and strictly k-dependent for total effect indices. In the present note we compare existing and new practices for this index and offer recommendations on which to use. ?? 2009 Elsevier B.V. All rights reserved.},
author = {Saltelli, A. and Annoni, P. and Azzini, I. and Campolongo, F. and Ratto, M. and Tarantola, S.},
doi = {10.1016/j.cpc.2009.09.018},
file = {:Users/arnald/Library/Application Support/Mendeley Desktop/Downloaded/Saltelli et al. - 2010 - Variance based sensitivity analysis of model output. Design and estimator for the total sensitivity index.pdf:pdf},
journal = {Computer Physics Communications},
number = {2},
pages = {259--270},
title = {{Variance based sensitivity analysis of model output. Design and estimator for the total sensitivity index}},
volume = {181},
year = {2010}
}
@article{KhorashadiZadeh2017,
abstract = {Global Sensitivity Analysis (GSA) is an essential technique to support the calibration of environmental models by identifying the influential parameters (screening) and ranking them. In this paper, the widely-used variance-based method (Sobol') and the recently proposed moment-independent PAWN method for GSA are applied to the Soil and Water Assessment Tool (SWAT), and compared in terms of ranking and screening results of 26 SWAT parameters. In order to set a threshold for parameter screening, we propose the use of a “dummy parameter”, which has no influence on the model output. The sensitivity index of the dummy parameter is calculated from sampled data, without changing the model equations. We find that Sobol' and PAWN identify the same 12 influential parameters but rank them differently, and discuss how this result may be related to the limitations of the Sobol' method when the output distribution is asymmetric.},
author = {{Khorashadi Zadeh}, F. and Nossent, J. and Sarrazin, F. and Pianosi, F. and van Griensven, A. and Wagener, T. and Bauwens, W.},
doi = {10.1016/j.envsoft.2017.02.001},
journal = {Environmental Modelling and Software},
keywords = {Global sensitivity analysis,Moment-independent method,PAWN,SWAT,Sobol',Variance-based method},
pages = {210--222},
publisher = {Elsevier Ltd},
title = {{Comparison of variance-based and moment-independent global sensitivity analysis approaches by application to the SWAT model}},
volume = {91},
year = {2017}
}
@article{Bratley1992,
author = {Bratley, P. and Fox, B. L. and Niederreiter, H.},
journal = {ACM Transactions on Modeling and Computer Simulation (TOMACS)},
number = {3},
pages = {195--213},
title = {{Implementation and tests of low-discrepancy sequences}},
volume = {2},
year = {1992}
}
@article{Oakley2004,
abstract = {Summary. In many areas of science and technology, mathematical models are built to simulate complex real world phenomena. Such models are typically implemented in large computer programs and are also very complex, such that the way that the model responds to changes in its inputs is not transparent. Sensitivity analysis is concerned with understanding how changes in the model inputs influence the outputs. This may be motivated simply by a wish to understand the implications of a complex model but often arises because there is uncertainty about the true values of the inputs that should be used for a particular application. A broad range of measures have been advocated in the literature to quantify and describe the sensitivity of a model's output to variation in its inputs. In practice the most commonly used measures are those that are based on formulating uncertainty in the model inputs by a joint probability distribution and then analysing the induced uncertainty in outputs, an approach which is known as probabilistic sensitivity analysis. We present a Bayesian framework which unifies the various tools of prob- abilistic sensitivity analysis. The Bayesian approach is computationally highly efficient. It allows effective sensitivity analysis to be achieved by using far smaller numbers of model runs than standard Monte Carlo methods. Furthermore, all measures of interest may be computed from a single set of runs.},
author = {Oakley, J.E. and O'Hagan, A.},
doi = {10.1111/j.1467-9868.2004.05304.x},
journal = {Journal of the Royal Statistical Society B},
keywords = {bayesian inference,computer model,gaussian process,sensitivity analysis,uncertainty analysis},
number = {3},
pages = {751--769},
title = {{Probabilistic sensitivity analysis of complex models: a Bayesian approach}},
volume = {66},
year = {2004}
}
@article{Bratley1988,
author = {Bratley, P. and Fox, B. L.},
journal = {ACM Transactions on Mathematical Software},
number = {1},
pages = {88--100},
title = {{Algorithm 659: Implementing Sobol's quasirandom sequence generator}},
volume = {14},
year = {1988}
}
@article{Ishigami1990,
author = {Ishigami, T. and Homma, T.},
journal = {Proceedings. First International Symposium on Uncertainty Modeling and Analysis},
pages = {398--403},
title = {{An importance quantification technique in uncertainty analysis for computer models}},
volume = {12},
year = {1990}
}
@article{Sobol1998,
author = {Sobol', I. M.},
doi = {10.1016/S0378-4754(98)00096-2},
journal = {Mathematics and Computers in Simulation},
month = {aug},
number = {2-5},
pages = {103--112},
title = {{On quasi-Monte Carlo integrations}},
volume = {47},
year = {1998}
}
@article{Sobol1967,
author = {Sobol', I.M},
doi = {10.1016/0041-5553(67)90144-9},
journal = {USSR Computational Mathematics and Mathematical Physics},
month = {jan},
number = {4},
pages = {86--112},
title = {{On the distribution of points in a cube and the approximate evaluation of integrals}},
volume = {7},
year = {1967}
}
@article{Janon2014,
abstract = {Many mathematical models involve input parameters, which are not precisely known. Global sensitivity analysis aims to identify the parameters whose uncertainty has the largest impact on the variability of a quantity of interest (output of the model). One of the statistical tools used to quantify the influence of each input variable on the output is the Sobol sensitivity index. We consider the statistical estimation of this index from a finite sample of model outputs: we present two estimators and state a central limit theorem for each. We show that one of these estimators has an optimal asymptotic variance. We also generalize our results to the case where the true output is not observable, and is replaced by a noisy version.},
author = {Janon, A. and Klein, T. and Lagnoux, A. and Nodet, M. and Prieur, C.},
doi = {10.1051/ps/2013040},
journal = {ESAIM: Probability and Statistics},
keywords = {and phrases,asymptotic efficiency,asymptotic normality,confidence,intervals,metamodelling,sensitivity analysis,sobol indices,surface response methodology},
number = {3},
pages = {342--364},
title = {{Asymptotic normality and efficiency of two Sobol index estimators}},
volume = {18},
year = {2014}
}
@article{Sobol1993,
abstract = {A theorem about decomposition of an integrable function into summands of different dimensions is proved. A Monte Carlo algorithm is proposed for estimating the sensitivity of a function with respect to arbitrary groups of variables.},
author = {Sobol', I. M.},
journal = {Mathematical Modeling and Computational Experiment},
keywords = {Anova,Sobol' sensitivity indices,Sobol' variance decomposition},
number = {4},
pages = {407--414},
title = {{Sensitivity analysis for nonlinear mathematical models}},
volume = {1},
year = {1993}
}
@article{Sobol2001,
abstract = {This is a review of global sensitivity indices that were introduced in I.M. Sobol' (1990). These indices allow to analyze numerically the structure of a nonlinear function defined analytically or by a “black box”. As an example the Brownian bridge is considered and an example of the application of global sensitivity indices in finance is presented.},
author = {Sobol', I.M},
doi = {10.1016/S0378-4754(00)00270-6},
journal = {Mathematics and Computers in Simulation},
keywords = {mathematical modelling,monte carlo method,quasi-monte carlo method,sensitivity analysis},
month = {feb},
number = {1-3},
pages = {271--280},
title = {{Global sensitivity indices for nonlinear mathematical models and their Monte Carlo estimates}},
volume = {55},
year = {2001}
}
@article{Homma1996,
abstract = {The present paper deals with a new method of global sensitivity analysis of nonlinear models. This is based on a measure of importance to calculate the fractional contribution of the input parameters to the variance of the model prediction. Measures of importance in sensitivity analysis have been suggested by several authors, whose work is reviewed in this article. More emphasis is given to the developments of sensitivity indices by the Russian mathematician I.M. Sobol'. Given that Sobol' treatment of the measure of importance is the most general, his formalism is employed throughout this paper where conceptual and computational improvements of the method are presented. The computational novelty of this study is the introduction of the 'total effect' parameter index. This index provides a measure of the total effect of a given parameter, including all the possible synergetic terms between that parameter and all the others. Rank transformation of the data is also introduced in order to increase the reproducibility of the method. These methods are tested on a few analytical and computer models. The main conclusion of this work is the identification of a sensitivity analysis methodology which is both flexible, accurate and informative, and which can be achieved at reasonable computational cost. (C) 1996 Elsevier Science Limited.},
author = {Homma, T. and Saltelli, A.},
doi = {10.1016/0951-8320(96)00002-6},
journal = {Reliability Engineering {\&} System Safety},
pages = {1--17},
title = {{Importance measures in global sensitivity analysis of nonlinear models}},
volume = {52},
year = {1996}
}
@article{Ludwig1976,
abstract = {(1) A procedure has been described for the qualitative analysis of$\backslash$ninsect outbreak systems using spruce budworm and balsam fir as an$\backslash$nexample. This consists of separating the state variables into fast$\backslash$nand slow categories. (2) The dynamics of the fast variables are analysed$\backslash$nfirst, holding the slow variables fixed. Then the dynamics of the$\backslash$nslow variables are analysed, with the fast variables held at corresponding$\backslash$nequilibrium values. If there are several such equilibria, there are$\backslash$nseveral possibilities for the slow dynamics. (3) In the case of the$\backslash$nbudworm, this analysis exhibits the possibility of `relaxation oscillations'$\backslash$nwhich are familiar from theory of the Van der Pol oscillator. In$\backslash$nmore modern terminology, the jumps of the system are governed by$\backslash$na cusp catastrophe. (4) Such an analysis can be made on the basis$\backslash$nof qualitative information only, but additional insight emerges when$\backslash$nparameter ranges are defined by the kind of information typically$\backslash$navailable from an experienced biologist. (5) At the least this can$\backslash$nbe a guide to assess subsequent priorities for both research and$\backslash$npolicy.},
author = {Ludwig, D. and Jones, D. D. and Holling, C. S.},
doi = {10.2307/3939},
journal = {The Journal of Animal Ecology},
number = {1},
pages = {315},
title = {{Qualitative analysis of insect outbreak systems: the spruce budworm and forest}},
volume = {47},
year = {1976}
}
@article{Azzini2020,
abstract = {This study compares the performances of two sampling-based strategies for the simultaneous estimation of the first-and total-orders variance-based sensitivity indices (a.k.a Sobol' indices). The first strategy was introduced by [8] and is the current approach employed by practitioners. The second one was only recently introduced by the authors of the present article. They both rely on different estimators of first-and total-orders Sobol' indices. The asymp-totic normal variances of the two sets of estimators are established and their accuracies are compared theoretically and numerically. The results show that the new strategy outperforms the current one.Keywords: global sensitivity analysis, variance-based sensitivity indices, first-order Sobol' index, total-order Sobol' index, Monte Carlo estimate, asymptotic normality},
journal = {arXiv},
author = {Azzini, Ivano and Mara, Thierry and Rosati, Rossana},
eprint = {2006.08232},
keywords = {asymptotic normality,first-order sobol,global sensitivity analysis,index,monte carlo estimate,total-order sobol,variance-based sensitivity indices},
title = {{Monte Carlo estimators of first-and total-orders Sobol' indices}},
url = {https://arxiv.org/abs/2006.08232},
year = {2020}
}
@article{Glen2012,
abstract = {Sensitivity analysis is a crucial tool in the development and evaluation of complex mathematical models. Sobol's method is a variance-based global sensitivity analysis technique that has been applied to computational models to assess the relative importance of input parameters on the output. This paper introduces new notation that describes the Sobol indices in terms of the Pearson correlation of outputs from pairs of runs, and introduces correction terms to remove some of the spurious correlation. A variety of estimation techniques are compared for accuracy and precision using the G function as a test case. {\textcopyright} 2012.},
author = {Glen, Graham and Isaacs, Kristin},
doi = {10.1016/j.envsoft.2012.03.014},
journal = {Environmental Modelling and Software},
keywords = {Monte Carlo modeling,Sensitivity analysis,Sobol's method},
pages = {157--166},
publisher = {Elsevier Ltd},
title = {{Estimating Sobol sensitivity indices using correlations}},
volume = {37},
year = {2012}
}
@book{Saltelli2008,
abstract = {1 Introduction to Sensitivity Analysis 1.1 Models and Sensitivity Analysis 1.1.1 Definition 1.1.2 Models 1.1.3 Models and Uncertainty 1.1.4 How to Set Up Uncertainty and Sensitivity Analyses 1.1.5 Implications for Model Quality 1.2 Methods and Settings for Sensitivity Analysis – an Introduction 1.2.1 Local versus Global 1.2.2 A Test Model 1.2.3 Scatterplots versus Derivatives 1.2.4 Sigma-normalized Derivatives 1.2.5 Monte Carlo and Linear Regression 1.2.6 Conditional Variances – First Path 1.2.7 Conditional Variances – Second Path 1.2.8 Application to Model (1.3) 1.2.9 A First Setting: ‘Factor Prioritization' 1.2.10 Nonadditive Models 1.2.11 Higher-order Sensitivity Indices 1.2.12 Total Effects 1.2.13 A Second Setting: ‘Factor Fixing' 1.2.14 Rationale for Sensitivity Analysis 1.2.15 Treating Sets 1.2.16 Further Methods 1.2.17 Elementary Effect Test 1.2.18 Monte Carlo Filtering 1.3 Nonindependent Input Factors 1.4 Possible Pitfalls for a Sensitivity Analysis 1.5 Concluding Remarks; 1.6 Exercises 1.7 Answers 1.8 Additional Exercises 1.9 Solutions to Additional Exercises 2 Experimental Designs 2.1 Introduction 2.2 Dependency on a Single Parameter 2.3 Sensitivity Analysis of a Single Parameter 2.3.1 Random Values 2.3.2 Stratified Sampling 2.3.3 Mean and Variance Estimates for Stratified Sampling 2.4 Sensitivity Analysis of Multiple Parameters 2.4.1 Linear Models 2.4.2 One-at-a-time (OAT) Sampling 2.4.3 Limits on the Number of Influential Parameters 2.4.4 Fractional Factorial Sampling 2.4.5 Latin Hypercube Sampling 2.4.6 Multivariate Stratified Sampling 2.4.7 Quasi-random Sampling with Low-discrepancy Sequences 2.5 Group Sampling 2.6 Exercises 2.7 Exercise Solutions 3 Elementary Effects Method 3.1 Introduction 3.2 The Elementary Effects Method 3.3 The Sampling Strategy and its Optimization 3.4 The Computation of the Sensitivity Measures 3.5 Working with Groups 3.6 The EE Method Step by Step 3.7 Conclusions 3.8 Exercises 3.9 Solutions 4 Variance-based Methods 4.1 Different Tests for Different Settings 4.2 Why Variance? 4.3 Variance-based Methods. A Brief History 4.4 Interaction Effects 4.5 Total Effects 4.6 How to Compute the Sensitivity Indices; 4.7 FAST and Random Balance Designs 4.8 Putting the Method to Work: The Infection Dynamics Model 4.9 Caveats 4.10 Exercises 5 Factor Mapping and Metamodelling With Peter Young 5.1 Introduction 5.2 Monte Carlo Filtering (MCF) 5.2.1 Implementation of Monte Carlo Filtering 5.2.2 Pros and Cons 5.2.3 Exercises 5.2.4 Solutions 5.2.5 Examples 5.3 Metamodelling and the High-Dimensional Model Representation 5.3.1 Estimating HDMRs and Metamodels 5.3.2 A Simple Example 5.3.3 Another Simple Example 5.3.4 Exercises 5.3.5 Solutions to Exercises 5.4 Conclusions 6 Sensitivity Analysis: From Theory to Practice 6.1 Example 1: A Composite Indicator 6.1.1 Setting the Problem 6.1.2 A Composite Indicator Measuring Countries' Performance in Environmental Sustainability 6.1.3 Selecting the Sensitivity Analysis Method 6.1.4 The Sensitivity Analysis Experiment and Results 6.1.5 Conclusions 6.2 Example 2: Importance of Jumps in Pricing Options 6.2.1 Setting the Problem 6.2.2 The Heston Stochastic Volatility Model with Jumps 6.3 Example 3: A Chemical Reactor 6.3.1 Setting the Problem 6.2.3 Selecting a Suitable Sensitivity Analysis Method 6.2.4 The Sensitivity Analysis Experiment and Results 6.2.5 Conclusions 6.3.2 Thermal Runaway Analysis of a Batch Reactor 6.3.3 Selecting the Sensitivity Analysis Method; 6.3.4 The Sensitivity Analysis Experiment and Results 6.3.5 Conclusions 6.4 Example 4: A Mixed Uncertainty–Sensitivity Plot 6.4.1 In Brief 6.5 When to use What?},
address = {Chichester, UK},
author = {Saltelli, Andrea and Ratto, Marco and Andres, Terry and Campolongo, Francesca and Cariboni, Jessica and Gatelli, Debora and Saisana, Michaela and Tarantola, Stefano},
doi = {10.1002/9780470725184},
month = {dec},
publisher = {John Wiley {\&} Sons, Ltd},
title = {{Global Sensitivity Analysis. The Primer}},
year = {2008}
}
@article{Sobol1976,
author = {Sobol', Ilya. M.},
doi = {10.1016/0041-5553(76)90154-3},
journal = {USSR Computational Mathematics and Mathematical Physics},
month = {jan},
number = {5},
pages = {236--242},
title = {{Uniformly distributed sequences with an additional uniform property}},
volume = {16},
year = {1976}
}
@article{McKay1979,
abstract = {Two types of sampling plans are examined as alternatives to simple random sampling in Monte Carlo studies. These plans are shown to be improvements over simple random sampling with respect to variance for a class of estimators which includes the sample mean and the empirical distribution function. {\textcopyright} 1979 Taylor {\&} Francis Group, LLC.},
author = {McKay, M. D. and Beckman, R. J. and Conover, W. J.},
doi = {10.1080/00401706.1979.10489755},
journal = {Technometrics},
keywords = {Latin hypercube sampling,Sampling techniques,Simulation techniques,Variance reduction},
number = {2},
pages = {239--245},
title = {{Comparison of three methods for selecting values of input variables in the analysis of output from a computer code}},
volume = {21},
year = {1979}
}
@article{Puyj,
abstract = {Sensitivity analysis helps decision-makers to understand how a given model output responds when there is variation in the model inputs. One of the most authoritative measures in global sensitivity analysis is the Sobol' total-order index ({\$}T{\_}i{\$}), which can be computed with several different estimators. Although previous comparisons exist, it is hard to know which estimator performs best since the results are contingent on several benchmark settings: the sampling method ({\$}\backslashtau{\$}), the distribution of the model inputs ({\$}\backslashphi{\$}), the number of model runs ({\$}N{\_}t{\$}), the test function or model ({\$}\backslashvarepsilon{\$}) and its dimensionality ({\$}k{\$}), the weight of higher order effects (e.g. second, third, {\$}k{\_}2,k{\_}3{\$}), or the performance measure selected ({\$}\backslashdelta{\$}). Here we break these limitations and simultaneously assess all total-order estimators in an eight-dimension hypercube where {\$}(\backslashtau, \backslashphi, N{\_}t, \backslashvarepsilon, k, k{\_}2, k{\_}3, \backslashdelta){\$} are treated as random parameters. This design allows to create an unprecedentedly large range of benchmark scenarios. Our results indicate that, in general, the preferred estimator should be Razavi and Gupta's, followed by that of Jansen, or Janon/Monod. The remainder lag significantly behind in performance. Our work helps analysts navigate the myriad of total-order formulae by effectively eliminating the uncertainty in the selection of the best estimator.},
archivePrefix = {arXiv},
arxivId = {2009.01147},
journal = {arXiv},
author = {Puy, Arnald and Becker, William and Piano, Samuele Lo and Saltelli, Andrea},
eprint = {2009.01147},
month = {sep},
title = {{The battle of total-order sensitivity estimators}},
url = {https://arxiv.org/abs/2009.01147},
year = {2020}
}
@article{Puyz,
abstract = {Sensitivity analysis helps decision-makers to understand how a given model output responds when there is variation in the model inputs. One of the most authoritative measures in global sensitivity analysis is the Sobol' total-order index ({\$}T{\_}i{\$}), which can be computed with several different estimators. Although previous comparisons exist, it is hard to know which estimator performs best since the results are contingent on several benchmark settings: the sampling method ({\$}\backslashtau{\$}), the distribution of the model inputs ({\$}\backslashphi{\$}), the number of model runs ({\$}N{\_}t{\$}), the test function or model ({\$}\backslashvarepsilon{\$}) and its dimensionality ({\$}k{\$}), the weight of higher order effects (e.g. second, third, {\$}k{\_}2,k{\_}3{\$}), or the performance measure selected ({\$}\backslashdelta{\$}). Here we break these limitations and simultaneously assess all total-order estimators in an eight-dimension hypercube where {\$}(\backslashtau, \backslashphi, N{\_}t, \backslashvarepsilon, k, k{\_}2, k{\_}3, \backslashdelta){\$} are treated as random parameters. This design allows to create an unprecedentedly large range of benchmark scenarios. Our results indicate that, in general, the preferred estimator should be Razavi and Gupta's, followed by that of Jansen, or Janon/Monod. The remainder lag significantly behind in performance. Our work helps analysts navigate the myriad of total-order formulae by effectively eliminating the uncertainty in the selection of the best estimator.},
archivePrefix = {arXiv},
doi = {10.1615/Int.J.UncertaintyQuantification.2021038133},
author = {Puy, Arnald and Becker, William and Lo Piano, Samuele and Saltelli, Andrea},
journal = {International Journal for Uncertainty Quantification},
title = {{A Comprehensive Comparison of Total-Order Estimators for Global Sensitivity Analysis}},
year = {2021}
}
@article{Becker2020,
abstract = {Comparison studies of global sensitivity analysis (GSA) approaches are limited in that they are performed on a single model or a small set of test functions, with a limited set of sample sizes and dimensionalities. This work introduces a flexible ‘metafunction' framework to benchmarking which randomly generates test problems of varying dimensionality and functional form using random combinations of plausible basis functions, and a range of sample sizes. The metafunction is tuned to mimic the characteristics of real models, in terms of the type of model response and the proportion of active model inputs. To demonstrate the framework, a comprehensive comparison of ten GSA approaches is performed in the screening setting, considering functions with up to 100 dimensions and up to 1000 model runs. The methods examined range from recent metamodelling approaches to elementary effects and Monte Carlo estimators of the Sobol' total effect index. The results give a comparison in unprecedented depth, and show that on average and in the setting investigated, Monte Carlo estimators, particularly the VARS estimator, outperform metamodels. Indicatively, metamodels become competitive at around 10–20 runs per model input, but at lower ratios sampling-based approaches are more effective as a screening tool.},
author = {Becker, William},
doi = {10.1016/j.ress.2020.107189},
journal = {Reliability Engineering and System Safety},
keywords = {Emulators,Gaussian process,Metamodels,Polynomial chaos,Sensitivity analysis},
pages = {107189},
publisher = {Elsevier Ltd},
title = {{Metafunctions for benchmarking in sensitivity analysis}},
volume = {204},
year = {2020}
}
@article{Razavi2016a,
abstract = {We have only rudimentary understanding of the complex and pervasive connections between water and energy in cities. As water security now threatens energy and economic security, this is a major omission. Understanding the water-energy nexus is necessary if we want to contribute to solving water and energy issues simultaneously; if we want to stop moving problems from one resource dimension to another. This is particularly relevant in the Australian context where energy use for water supplies is forecast to rapidly escalate, growing around 300{\%} from 2007 levels, by 2030. This paper presents a literature review with an aim of characterising the research to date with a particular focus on cities, the major centres of consumption and growth. It systematically analyses a wide range of papers and summarises the diverse objectives, dimensions, and scale of the research to-date together with knowledge gaps. There are many major gaps. These include energy use associated with water in industrial and commercial operations as well as socio-political perspectives. A major gap is the lack of a unifying theoretical framework and consistent methodology for analysis. This is considered a prerequisite for quantitative trans-city comparisons.},
archivePrefix = {arXiv},
arxivId = {10.1002/2014WR016527},
author = {Razavi, Saman and Gupta, Hoshin V.},
doi = {10.1002/2015WR017558},
eprint = {2014WR016527},
journal = {Water Resources Research},
keywords = {Cities,Environment,Labor,Livelihoods,Natural resources,Poverty,Review,Soils,Urban metabolism,Water energy nexus},
month = {jan},
number = {1},
pages = {440--455},
primaryClass = {10.1002},
title = {{A new framework for comprehensive, robust, and efficient global sensitivity analysis: 2. Application}},
volume = {52},
year = {2016}
}
@article{Razavi2016b,
abstract = {Based on the theoretical framework for sensitivity analysis called ‘‘Variogram Analysis of Response Surfaces'' (VARS), developed in the companion paper, we develop and implement a practical ‘‘star-based'' sampling strategy (called STAR-VARS), for the application of VARS to real-world problems. We also develop a bootstrap approach to provide confidence level estimates for the VARS sensitivity metrics and to evaluate the reliability of inferred factor rankings. The effectiveness, efficiency, and robustness of STAR-VARS are demonstrated via two real-data hydrological case studies (a 5-parameter conceptual rainfall- runoff model and a 45-parameter land surface scheme hydrology model), and a comparison with the ‘‘derivative-based'' Morris and ‘‘variance-based'' Sobol approaches are provided. Our results show that STAR- VARS provides reliable and stable assessments of ‘‘global'' sensitivity across the full range of scales in the factor space, while being 1–2 orders of magnitude more efficient than the Morris or Sobol approaches. Citation:},
author = {Razavi, Saman and Gupta, Hoshin V.},
doi = {10.1002/2015WR017559},
journal = {Water Resources Research},
month = {jan},
number = {1},
pages = {423--439},
title = {{A new framework for comprehensive, robust, and efficient global sensitivity analysis: 1. Theory}},
volume = {52},
year = {2016}
}
@article{Saltelli2010b,
abstract = {Mathematical modelers from different disciplines and regulatory agencies worldwide agree on the importance of a careful sensitivity analysis (SA) of model-based inference. The most popular SA practice seen in the literature is that of 'one-factor-at-a-time' (OAT). This consists of analyzing the effect of varying one model input factor at a time while keeping all other fixed. While the shortcomings of OAT are known from the statistical literature, its widespread use among modelers raises concern on the quality of the associated sensitivity analyses. The present paper introduces a novel geometric proof of the inefficiency of OAT, with the purpose of providing the modeling community with a convincing and possibly definitive argument against OAT. Alternatives to OAT are indicated which are based on statistical theory, drawing from experimental design, regression analysis and sensitivity analysis proper. {\textcopyright} 2010 Elsevier Ltd.},
author = {Saltelli, A. and Annoni, P.},
doi = {10.1016/j.envsoft.2010.04.012},
journal = {Environmental Modelling and Software},
keywords = {Mathematical modeling,One-at-a-time,Robustness,Sensitivity analysis,Uncertainty analysis},
number = {12},
pages = {1508--1517},
title = {{How to avoid a perfunctory sensitivity analysis}},
volume = {25},
year = {2010}
}
@article{Kucherenko2011,
author = {Kucherenko, S. and Feil, B. and Shah, N. and Mauntz, W.},
doi = {10.1016/j.ress.2010.11.003},
file = {:Users/arnald/Library/Application Support/Mendeley Desktop/Downloaded/Kucherenko et al. - 2011 - The identification of model effective dimensions using global sensitivity analysis.pdf:pdf},
issn = {09518320},
journal = {Reliability Engineering {\&} System Safety},
keywords = {2004,Effective dimensions,Global sensitivity analysis,Monte Carlo integration,Quasi-Monte Carlo,Sobol' sensitivity indices,monte carlo integration},
mendeley-tags = {2004},
month = {apr},
number = {4},
pages = {440--449},
publisher = {Elsevier},
title = {{The identification of model effective dimensions using global sensitivity analysis}},
volume = {96},
year = {2011}
}
