A new variance-based global sensitivity analysis technique

A new set of variance-based sensitivity indices, called W$W$-indices, is proposed. Similar to the Sobol’s indices, both main and total effect indices are defined. The W$W$-main effect indices measure the average reduction of model output variance when the ranges of a set of inputs are reduced, and the total effect indices quantify the average residual variance when the ranges of the remaining inputs are reduced. Geometrical interpretations show that the W$W$-indices gather the full information of the variance ratio function, whereas, Sobol’s indices only reflect the marginal information. Then the double-loop-repeated-set Monte Carlo (MC) (denoted as DLRS MC) procedure, the double-loop-single-set MC (denoted as DLSS MC) procedure and the model emulation procedure are introduced for estimating the W$W$-indices. It is shown that the DLRS MC procedure is suitable for computing all the W$W$-indices despite its highly computational cost. The DLSS MC procedure is computationally efficient, however, it is only applicable for computing low order indices. The model emulation is able to estimate all the W$W$-indices with low computational cost as long as the model behavior is correctly captured by the emulator. The Ishigami function, a modified Sobol’s function and two engineering models are utilized for comparing the W$W$- and Sobol’s indices and verifying the efficiency and convergence of the three numerical methods. Results show that, for even an additive model, the W$W$-total effect index of one input may be significantly larger than its W$W$-main effect index. This indicates that there may exist interaction effects among the inputs of an additive model when their distribution ranges are reduced.     

Using multiple models to uncover blood vessel patterns in color images for forensic analysis

With the proliferation of digital cameras, images of crimes, such as child sexual abuse images, are increasing dramatically. Both verification and identification of criminals and victims in these images are highly difficult and often impossible for the current biometric technology because their faces, tattoos, and distinctive skin mark patterns are not always observable. Superficial blood vessels under skin are a potential solution to compensate the weaknesses of the traditional biometric traits. However, blood vessels were neglected by law enforcement agencies because they are generally invisible in color images. To use blood vessel patterns in forensic analysis, this paper proposes three computational models to uncover hidden patterns, two optimization schemes to handle illumination variations and prevent over-relying on biophysical parameters measured in ideal medical conditions, a matching algorithm to automatically extract and compare noisy patterns, and two fusion rules to combine patterns from the three models for performance enhancement. The experimental results on 1900 color images and 1900 infrared images from 490 forearms and 460 thighs show that the matching performance of the blood vessel patterns from the color images is comparable with that from the infrared images. The proposed models are also applied to hands, arms, thighs, chests, breasts, and abdomens of men, women, and children in indoor and outdoor images collected from the Internet. Though these images were taken in uncontrolled environments and the subjects had different poses, the proposed models can uncover blood vessels. These results indicate that the potential of using blood vessel patterns in forensic analysis was underestimated.     

Comparison of variance-based and moment-independent global sensitivity analysis approaches by application to the SWAT model

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.     

A spatially explicit agent-based simulation platform for investigating effects of shared pollination service on ecological communities

The alarming reports from around the world on pollinator population declines made the understanding of the effects of shared pollination service on biodiversity into one of the most urgent goals in nature conservation, both for the scientists and managers. The classic field-based methodology which is commonly used in such studies, has three major problems which limit the researchers’ ability to further understand the nature of plant-pollinator dynamics: (1) Natural systems do not allow for a full factorial controlled studies of specific characteristics and traits of both plants and pollinators, because of many confounding effects which are usually unknown. Furthermore, (2) Many of the interactions between plants and pollinators are indirect, via their reciprocal effect on shared pollination services and therefore difficult to detect in the field. Finally, and (3) though plant composition and abundance may be manipulated in the field, it is almost impossible to manipulate pollinator populations, strongly restricting researchers’ ability to thoroughly understand the specific pollinator characteristics which created the observed effects. Therefore, simulation tools are needed that can address this complexity on one hand, and allow to identify potential research directions for targeted experiments on the other hand. Here, we present EcoSimInGrid, a spatially explicit agent-based simulator for investigating effects of shared pollination services on plant communities. EcoSimInGrid can be used to represent complex spatio-temporal interactions among ecological entities of different trophic levels, to investigate effects of plant traits, spatial distribution and pollinator behavior on shared pollination services and to analyze the relative effects of shared pollination and habitat productivity in shaping community diversity. Features like capability to model large ecosystems with tens of thousands of plants and pollinators, graphical user interface, flexible parameter configuration, comprehensive data output and fast speed parallel computing make EcoSimInGrid a welcome addition to the ecological modeling world.     

A spatially explicit agent-based modeling approach for the spread of Cutaneous Leishmaniasis disease in central Iran,Isfahan

Cutaneous Leishmaniasis (CL) is an endemic vector-borne disease in the Middle East and a worldwide public health problem. The spread of CL is highly associated with the socio-ecological interactions of vectors, hosts and the environment. The heterogeneity of these interactions has hindered CL modeling for healthcare preventive measures in endemic areas. In this study, an agent-based model (ABM) is developed to simulate the dynamics of CL spread based on a Geographic Automata System (GAS). A Susceptible-Exposed-Infected-Recovered (SEIR) approach together with Bayesian modeling has been applied in the ABM to explore the spread of CL. The model is then adapted locally for Isfahan Province, an endemic area in central Iran. The results from the model indicate that desertification areas are the main origin of CL, and riverside population centers have the potential to host more sand fly exposures and should receive more preventive measures from healthcare authorities. The results also show that healthcare service accessibility prevented exposures from becoming infected and areas with new inhabitants experienced more infections from same amount of sand fly exposures.     

Multivariate global sensitivity analysis for dynamic models based on energy distance

In this paper, a new kind of multivariate global sensitivity index based on energy distance is proposed. The covariance decomposition based index has been widely used for multivariate global sensitivity analysis. However, it just considers the variance of multivariate model output and ignores the correlation between different outputs. The proposed index considers the whole probability distribution of dynamic output based on characteristic function and contains more information of uncertainty than the covariance decomposition based index. The multivariate probability integral transformation based index is an extension of the popularly used moment-independent sensitivity analysis index. Although it considers the whole probability distribution of dynamic output, it is difficult to estimate the joint cumulative distribution function of dynamic output. The proposed sensitivity index can be easily estimated, especially for models with high dimensional outputs. Compared to the classic sensitivity indices, the proposed sensitivity index can be easily used for dynamic systems and obtain reasonable results. An efficient method based on the idea of the given-data method is used to estimate the proposed sensitivity index with only one set of input-output samples. The numerical and engineering examples are employed to compare the proposed index and the covariance decomposition based index. The results show that the input variables may have different effect on the whole probability distribution and variance of dynamic model output since the proposed index and the covariance decomposition based index measure the effects of input variables on the whole distribution and variance of model output separately.     

Distance correlation-based method for global sensitivity analysis of models with dependent inputs

Structural and Multidisciplinary Optimization - Global sensitivity analysis (GSA) plays an important role to quantify the relative importance of uncertain parameters to the model response. However,...     

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.     

Identifying parametric controls and dependencies in integrated assessment models using global sensitivity analysis

Integrated assessment models for climate change (IAMs) couple representations of economic and natural systems to identify and evaluate strategies for managing the effects of global climate change. In this study we subject three policy scenarios from the globally-aggregated Dynamic Integrated model of Climate and the Economy IAM to a comprehensive global sensitivity analysis using Sobol' variance decomposition. We focus on cost metrics representing diversions of economic resources from global world production. Our study illustrates how the sensitivity ranking of model parameters differs for alternative cost metrics, over time, and for different emission control strategies. This study contributes a comprehensive illustration of the negative consequences associated with using a priori expert elicitations to reduce the set of parameters analyzed in IAM uncertainty analysis. The results also provide a strong argument for conducting comprehensive model diagnostics for IAMs that explicitly account for the parameter interactions between the coupled natural and economic system components.     

Estimating joinpoints in continuous time scale for multiple change-point models

Joinpoint models have been applied to the cancer incidence and mortality data with continuous change points. The current estimation method [Lerman, P.M., 1980. Fitting segmented regression models by grid search. Appl. Statist. 29, 77-84] assumes that the joinpoints only occur at discrete grid points. However, it is more realistic that the joinpoints take any value within the observed data range. Hudson [1966. Fitting segmented curves whose join points have to be estimated. J. Amer. Statist. Soc. 61, 1097-1129] provides an algorithm to find the weighted least square estimates of the joinpoint on the continuous scale. Hudson described the estimation procedure in detail for a model with only one joinpoint, but its extension to a multiple joinpoint model is not straightforward. In this article, we describe in detail Hudson's method for the multiple joinpoint model and discuss issues in the implementation. We compare the computational efficiencies of the LGS method and Hudson's method. The comparisons between the proposed estimation method and several alternative approaches, especially the Bayesian joinpoint models, are discussed. Hudson's method is implemented by C++ and applied to the colorectal cancer incidence data for men under age 65 from SEER nine registries.     

Estimation of global sensitivity indices for models with dependent variables

A novel approach for estimation variance-based sensitivity indices for models with dependent variables is presented. Both the first order and total sensitivity indices are derived as generalizations of Sobol? sensitivity indices. Formulas and Monte Carlo numerical estimates similar to Sobol? formulas are derived. A copula-based approach is proposed for sampling from arbitrary multivariate probability distributions. A good agreement between analytical and numerical values of the first order and total indices for considered test cases is obtained. The behavior of sensitivity indices depends on the relative predominance of interactions and correlations. The method is shown to be efficient and general.     

Efficient sampling methods for global reliability sensitivity analysis

An important problem in structure reliability analysis is how to reduce the failure probability. In this work, we introduce a main and total effect indices framework of global reliability sensitivity. By decreasing the uncertainty of input variables with high main effect indices, the most reduction of failure probability can be obtained. By decreasing the uncertainty of the input variables with small total effect indices (close to zero), the failure probability will not be reduced significantly. The efficient sampling methods for evaluating the main and total effect indices are presented. For the problem with large failure probability, a single-loop Monte Carlo simulation (MCS) is derived for computing these sensitivity indices. For the problem with small failure probability, the single-loop sampling methods combined with the importance sampling procedure (IS) and the truncated importance sampling procedure (TIS) respectively are derived for improving the calculation efficiency. Two numerical examples and one engineering example are introduced for demonstrating the efficiency and precision of the calculation methods and illustrating the engineering significance of the global reliability sensitivity indices.     

A global sensitivity analysis in structural mechanics

A methodology is developed to evaluate the response sensitivity of structural systems to variations in their design parameters. The sensitivity is evaluated by considering the global behavior of the system response when the parameters vary within a bounded region. The design parameters are characterized by means of baseline values plus fluctuating components, and the sensitivity of the system is measured in terms of the global variability of the response with respect to its baseline response. The methodology is then extended into the context of optimum redesign analysis of structural systems. Application of the method is made to a structural system defined by two-dimensional beam-column elements and to a system defined by plate elements. The numerical implementation of the global sensitivity approach is made by means of the finite element method. Several analyses are performed and the results are discussed. Finally, some extensions of the present work are presented.     

Using a Bayesian framework and global sensitivity analysis to identify strengths and weaknesses of two process-based models differing in representation of autotrophic respiration

Process-based models are powerful tools for sustainable and adaptive forest management. Bayesian statistics and global sensitivity analysis allow to reduce uncertainties in parameters and outputs, and they provide better insight of model behaviour. In this work two versions of a process-based model that differed in the autotrophic respiration modelling were analysed. The original version (3PGN) was based on a constant ratio between net and gross primary production, while in a new version (3PGN¹) the autotrophic respiration was modelled as a function of temperature and biomass. A Bayesian framework, and a global sensitivity analysis (Morris method) were used to reduce parametric uncertainty, to highlight strengths and weaknesses of the models and to evaluate their performances. The Bayesian approach allowed also to identify the weaknesses and strengths of the dataset used for the analyses. The Morris method in combination with the Bayesian framework helped to identify key parameters and gave a deeper understanding of model behaviour. Both model versions reliably predicted average stand diameter at breast height, average stand height, stand volume and stem biomass. On the contrary, the models were not able to accurately predict net ecosystem production. Bayesian model comparison showed that 3PGN¹, with the new autotrophic respiration model, has a higher conditional probability of being correct than the original 3PGN model.     

Fixed-priority sensitivity analysis for linear compute time models

Several formal results exist that allow an analytic determination of whether a particular scheduling discipline can feasibly schedule a given set of hard real-time periodic tasks. In most cases, these results provide little more than a `yes' or `no' answer. In practice, it is also useful to know how sensitive scheduling feasibility is to changes in the characteristics of the task set. This paper presents algorithms that allow a system developer to determine, for fixed-priority preemptive scheduling of hard real-time periodic tasks on a uniprocessor, how sensitive schedule feasibility is to changes in the computation times of various software components. The algorithms allow a system developer to determine what changes in task computation times can be made while preserving schedule feasibility (or what changes are needed to achieve feasibility). Both changes to the computation time of a single task and changes to the computation times of a specified subset of the tasks are analyzable. The algorithms also allow a decomposition of tasks into modules, where a module may be a component of multiple tasks     

Probabilistic sensitivity analysis methods for general decision models

Probabilistic sensitivity analysis has previously been described for the special case of dichotomous decision trees. We now generalize these techniques for a wider range of decision problems. These methods of sensitivity analysis allow the analyst to evaluate the impact of the multivariate uncertainty in the data used in the decision model and to gain insight into the probabilistic contribution of each of the variables to the decision outcome. The techniques are illustrated using Monte Carlo simulation on a trichotomous decision tree. Application of these powerful tools permits the decision analyst to investigate the structure and limitations of more complex decision problems with inherent uncertainties in the data upon which the decisions are based. Probabilistic sensitivity measures can provide guidance into the allocation of resources to resolve uncertainty about critical components of medical decisions.     

A General Probabilistic Framework for uncertainty and global sensitivity analysis of deterministic models: A hydrological case study

The present study proposes a General Probabilistic Framework (GPF) for uncertainty and global sensitivity analysis of deterministic models in which, in addition to scalar inputs, non-scalar and correlated inputs can be considered as well. The analysis is conducted with the variance-based approach of Sobol/Saltelli where first and total sensitivity indices are estimated. The results of the framework can be used in a loop for model improvement, parameter estimation or model simplification. The framework is applied to SWAP, a 1D hydrological model for the transport of water, solutes and heat in unsaturated and saturated soils. The sources of uncertainty are grouped in five main classes: model structure (soil discretization), input (weather data), time-varying (crop) parameters, scalar parameters (soil properties) and observations (measured soil moisture). For each source of uncertainty, different realizations are created based on direct monitoring activities. Uncertainty of evapotranspiration, soil moisture in the root zone and bottom fluxes below the root zone are considered in the analysis. The results show that the sources of uncertainty are different for each output considered and it is necessary to consider multiple output variables for a proper assessment of the model. Improvements on the performance of the model can be achieved reducing the uncertainty in the observations, in the soil parameters and in the weather data. Overall, the study shows the capability of the GPF to quantify the relative contribution of the different sources of uncertainty and to identify the priorities required to improve the performance of the model. The proposed framework can be extended to a wide variety of modelling applications, also when direct measurements of model output are not available.