scholarly journals An Application of Monte-Carlo-Based Sensitivity Analysis on the Overlap in Discriminant Analysis

2012 ◽  
Vol 2012 ◽  
pp. 1-14 ◽  
Author(s):  
S. Razmyan ◽  
F. Hosseinzadeh Lotfi
Keyword(s):  
Decision Making ◽  
Sensitivity Analysis ◽  
Monte Carlo ◽  
Discriminant Analysis ◽  
Uncertain Variable ◽  
Model Parameters ◽  
Sampled Data ◽  
First Order ◽  
Sensitivity Indices ◽  
Input Variables

Discriminant analysis (DA) is used for the measurement of estimates of a discriminant function by minimizing their group misclassifications to predict group membership of newly sampled data. A major source of misclassification in DA is due to the overlapping of groups. The uncertainty in the input variables and model parameters needs to be properly characterized in decision making. This study combines DEA-DA with a sensitivity analysis approach to an assessment of the influence of banks’ variables on the overall variance in overlap in a DA in order to determine which variables are most significant. A Monte-Carlo-based sensitivity analysis is considered for computing the set of first-order sensitivity indices of the variables to estimate the contribution of each uncertain variable. The results show that the uncertainties in the loans granted and different deposit variables are more significant than uncertainties in other banks’ variables in decision making.

scholarly journals New Importance Measures Based on Failure Probability in Global Sensitivity Analysis of Reliability

Mathematics ◽  
2021 ◽  
Vol 9 (19) ◽  
pp. 2425
Author(s):  
Zdeněk Kala
Keyword(s):  
Sensitivity Analysis ◽  
Global Sensitivity Analysis ◽  
Binary Outcome ◽  
Global Sensitivity ◽  
First Order ◽  
Sensitivity Measure ◽  
Sensitivity Indices ◽  
Alternative Measures ◽  
Input Variables ◽  
Dome Shape

This article presents new sensitivity measures in reliability-oriented global sensitivity analysis. The obtained results show that the contrast and the newly proposed sensitivity measures (entropy and two others) effectively describe the influence of input random variables on the probability of failure Pf. The contrast sensitivity measure builds on Sobol, using the variance of the binary outcome as either a success (0) or a failure (1). In Bernoulli distribution, variance Pf(1 − Pf) and discrete entropy—Pfln(Pf) − (1 − Pf)ln(1 − Pf) are similar to dome functions. By replacing the variance with discrete entropy, a new alternative sensitivity measure is obtained, and then two additional new alternative measures are derived. It is shown that the desired property of all the measures is a dome shape; the rise is not important. Although the decomposition of sensitivity indices with alternative measures is not proven, the case studies suggest a rationale structure of all the indices in the sensitivity analysis of small Pf. The sensitivity ranking of input variables based on the total indices is approximately the same, but the proportions of the first-order and the higher-order indices are very different. Discrete entropy gives significantly higher proportions of first-order sensitivity indices than the other sensitivity measures, presenting entropy as an interesting new sensitivity measure of engineering reliability.

Disentangling uncertainties in risk-based planning of water resources in the UK

2021 ◽  
Author(s):  
Francesca Pianosi ◽  
Andres Penuela-Fernandez ◽  
Christopher Hutton
Keyword(s):  
Decision Making ◽  
Sensitivity Analysis ◽  
Monte Carlo ◽  
Water Resources ◽  
Water Resources Planning ◽  
Adaptive Planning ◽  
Water Companies ◽  
The Uk ◽  
Resources Planning

<p>Proper consideration of uncertainty has become a cornerstone of model-informed planning of water resource systems. In the UK Government’s 2020 Water Resources Planning Guidelines, the word “uncertainty” appears 48 times in 82 pages. This emphasis on uncertainty aligns with the increasing adoption by UK water companies of a “risk-based” approach to their long-term decision-making, in order to handle uncertainties in supply-demand estimation, climate change, population growth, etc. The term “risk-based” covers a range of methods - such as “info-gap”, “robust decision-making” or “system sensitivity analysis” - that come under different names but largely share a common rationale, essentially based on the use of Monte Carlo simulation. This shift in thinking from previous (deterministic) “worst-case” approach to a “risk-based” one is important and has the potential to significantly improve water resources planning practice. However its implementation is diminished by a certain lack of clarity about the terminology in use and about the concrete differences (and similarities) among methods. On top of these difficulties, in the next planning-cycle (2021-2026) two further step changes are introduced: (1) water companies are requested to move from a cost-efficiency approach focused on achieving the supply-demand balance, towards a fully multi-criteria approach that more explicitly encompasses other objectives including environmental sustainability; (2) as a further way to handle long-term uncertainties, they are required to embrace an “adaptive planning” approach. These changes will introduce two new sets of uncertainties around the robust quantification of criteria, particularly environmental ones, and around the attribution of weights to different criteria. This urgently calls for establishing structured approaches to quantify not only the uncertainty in model outputs, but also the sensitivity of those outputs to different forms of uncertainty in the modelling chain that mostly control the variability of the final outcome – the “best value” plan. Without this understanding of critical uncertainties, the risk is that huge efforts are invested on characterising and/or reducing uncertainties that later turn out to have little impact on the final outcome; or that water managers fall back to using oversimplified representation of those uncertainties as a way to escape the huge modelling burden. In this work, we aim at starting to establish a common rationale to “risk-based” methods within the context of a fully multi-criteria approach. We use a proof-of-concept example of a reservoir system in the South-West of England to demonstrate the use of global (i.e. Monte Carlo based) sensitivity analysis to simultaneously quantify output uncertainty and sensitivity, and identify robust decisions. We also discuss the potential of this approach to inform the construction of a “decision tree” for adaptive planning.</p>

Comprehensive global sensitivity analysis of a repository model using different types of transformations and metamodeling techniques

2021 ◽  
Author(s):  
Sabine M. Spiessl ◽  
Dirk-A. Becker ◽  
Sergei Kucherenko
Keyword(s):  
Sensitivity Analysis ◽  
Global Sensitivity Analysis ◽  
Higher Order ◽  
Model Parameters ◽  
High Dimensional Model Representation ◽  
Model Output ◽  
Global Sensitivity ◽  
Sparse Polynomial ◽  
Sensitivity Indices ◽  
Highly Nonlinear

<p>Due to their highly nonlinear, non-monotonic or even discontinuous behavior, sensitivity analysis of final repository models can be a demanding task. Most of the output of repository models is typically distributed over several orders of magnitude and highly skewed. Many values of a probabilistic investigation are very low or even zero. Although this is desirable in view of repository safety it can distort the evidence of sensitivity analysis. For the safety assessment of the system, the highest values of outputs are mainly essential and if those are only a few, their dependence on specific parameters may appear insignificant. By applying a transformation, different model output values are differently weighed, according to their magnitude, in sensitivity analysis. Probabilistic methods of higher-order sensitivity analysis, applied on appropriately transformed model output values, provide a possibility for more robust identification of relevant parameters and their interactions. This type of sensitivity analysis is typically done by decomposing the total unconditional variance of the model output into partial variances corresponding to different terms in the ANOVA decomposition. From this, sensitivity indices of increasing order can be computed. The key indices used most often are the first-order index (SI1) and the total-order index (SIT). SI1 refers to the individual impact of one parameter on the model and SIT represents the total effect of one parameter on the output in interactions with all other parameters. The second-order sensitivity indices (SI2) describe the interactions between two model parameters.</p><p>In this work global sensitivity analysis has been performed with three different kinds of output transformations (log, shifted and Box-Cox transformation) and two metamodeling approaches, namely the Random-Sampling High Dimensional Model Representation (RS-HDMR) [1] and the Bayesian Sparse PCE (BSPCE) [2] approaches. Both approaches are implemented in the SobolGSA software [3, 4] which was used in this work. We analyzed the time-dependent output with two approaches for sensitivity analysis, i.e., the pointwise and generalized approaches. With the pointwise approach, the output at each time step is analyzed independently. The generalized approach considers averaged output contributions at all previous time steps in the analysis of the current step. Obtained results indicate that robustness can be improved by using appropriate transformations and choice of coefficients for the transformation and the metamodel.</p><p>[1] M. Zuniga, S. Kucherenko, N. Shah (2013). Metamodelling with independent and dependent inputs. Computer Physics Communications, 184 (6): 1570-1580.</p><p>[2] Q. Shao, A. Younes, M. Fahs, T.A. Mara (2017). Bayesian sparse polynomial chaos expansion for global sensitivity analysis. Computer Methods in Applied Mechanics and Engineering, 318: 474-496.</p><p>[3] S. M. Spiessl, S. Kucherenko, D.-A. Becker, O. Zaccheus (2018). Higher-order sensitivity analysis of a final repository model with discontinuous behaviour. Reliability Engineering and System Safety, doi: https://doi.org/10.1016/j.ress.2018.12.004.</p><p>[4] SobolGSA software (2021). User manual https://www.imperial.ac.uk/process-systems-engineering/research/free-software/sobolgsa-software/.</p>

Sensitivity analysis and the challenges posed by multiple approaches: a multifaceted mess

2020 ◽  
Author(s):  
Monica Riva ◽  
Aronne Dell'Oca ◽  
Alberto Guadagnini
Keyword(s):  
Sensitivity Analysis ◽  
Model Calibration ◽  
Global Sensitivity Analysis ◽  
System Model ◽  
Model Parameters ◽  
Model Output ◽  
Multiple Model ◽  
Total Uncertainty ◽  
Global Sensitivity ◽  
Sensitivity Indices

<p>Modern models of environmental and industrial systems have reached a relatively high level of complexity. The latter aspect could hamper an unambiguous understanding of the functioning of a model, i.e., how it drives relationships and dependencies among inputs and outputs of interest. Sensitivity Analysis tools can be employed to examine this issue.</p><p>Global sensitivity analysis (GSA) approaches rest on the evaluation of sensitivity across the entire support within which system model parameters are supposed to vary. In this broad context, it is important to note that the definition of a sensitivity metric must be linked to the nature of the question(s) the GSA is meant to address. These include, for example: (i) which are the most important model parameters with respect to given model output(s)?; (ii) could we set some parameter(s) (thus assisting model calibration) at prescribed value(s) without significantly affecting model results?; (iii) at which space/time locations can one expect the highest sensitivity of model output(s) to model parameters and/or knowledge of which parameter(s) could be most beneficial for model calibration?</p><p>The variance-based Sobol’ Indices (e.g., Sobol, 2001) represent one of the most widespread GSA metrics, quantifying the average reduction in the variance of a model output stemming from knowledge of the input. Amongst other techniques, Dell’Oca et al. [2017] proposed a moment-based GSA approach which enables one to quantify the influence of uncertain model parameters on the (statistical) moments of a target model output.</p><p>Here, we embed in these sensitivity indices the effect of uncertainties both in the system model conceptualization and in the ensuing model(s) parameters. The study is grounded on the observation that physical processes and natural systems within which they take place are complex, rendering target state variables amenable to multiple interpretations and mathematical descriptions. As such, predictions and uncertainty analyses based on a single model formulation can result in statistical bias and possible misrepresentation of the total uncertainty, thus justifying the assessment of multiple model system conceptualizations. We then introduce copula-based sensitivity metrics which allow characterizing the global (with respect to the input) value of the sensitivity and the degree of variability (across the whole range of the input values) of the sensitivity for each value that the prescribed model output can possibly undertake, as driven by a governing model. In this sense, such an approach to sensitivity is global with respect to model input(s) and local with respect to model output, thus enabling one to discriminate the relevance of an input across the entire range of values of the modeling goal of interest. The methodology is demonstrated in the context of flow and reactive transport scenarios.</p><p> </p><p><strong>References</strong></p><p>Sobol, I. M., 2001. Global sensitivity indices for nonlinear mathematical models and their Monte Carlo estimates. Math. Comput. Sim., 55, 271-280.</p><p>Dell’Oca, A., Riva, M., Guadagnini, A., 2017. Moment-based metrics for global sensitivity analysis of hydrological systems. Hydr. Earth Syst. Sci., 21, 6219-6234.</p>

scholarly journals Global Sensitivity Analysis of Fuzzy Distribution Parameter on Failure Probability and Its Single-Loop Estimation

2014 ◽  
Vol 2014 ◽  
pp. 1-11 ◽  
Author(s):  
Lei Cheng ◽  
Zhenzhou Lu ◽  
Luyi Li
Keyword(s):  
Sensitivity Analysis ◽  
Failure Probability ◽  
Global Sensitivity Analysis ◽  
Computational Cost ◽  
Single Loop ◽  
Global Sensitivity ◽  
Sensitivity Indices ◽  
Distribution Parameters ◽  
Input Variables ◽  
Sampling Probability

An extending Borgonovo’s global sensitivity analysis is proposed to measure the influence of fuzzy distribution parameters on fuzzy failure probability by averaging the shift between the membership functions (MFs) of unconditional and conditional failure probability. The presented global sensitivity indices can reasonably reflect the influence of fuzzy-valued distribution parameters on the character of the failure probability, whereas solving the MFs of unconditional and conditional failure probability is time-consuming due to the involved multiple-loop sampling and optimization operators. To overcome the large computational cost, a single-loop simulation (SLS) is introduced to estimate the global sensitivity indices. By establishing a sampling probability density, only a set of samples of input variables are essential to evaluate the MFs of unconditional and conditional failure probability in the presented SLS method. Significance of the global sensitivity indices can be verified and demonstrated through several numerical and engineering examples.

Moment Matching for Sensitivity Analysis of Probabilistic Model Output

2004 ◽  
Author(s):  
Mahmoud Awad ◽  
Agus Sudjianto ◽  
Nanua Singh
Keyword(s):  
Sensitivity Analysis ◽  
Simulation Models ◽  
Moment Matching ◽  
Model Output ◽  
Sensitivity Indices ◽  
Variance Contribution ◽  
Complex Engineering ◽  
Input Variables ◽  
The Relationship ◽  
Effective Sensitivity

With the advent of highly complex engineering simulation models that describe the relationship between input variables and output response, the need for an efficient and effective sensitivity analysis is more demanding. In this article, a generalized approach that can provide efficient as well as accurate global sensitivity indices is developed. The approach consists of two steps: running an orthogonal array based experiment using moment-matched levels of the input variables and followed by a variance contribution analysis. The benefits of the approach are demonstrated through three different examples.

scholarly journals PROBABILISTIC ANALYSIS OP SEAFLOOR LIQUEFACTION

1988 ◽  
Vol 1 (21) ◽  
pp. 101 ◽  
Author(s):  
Rafael Blazquez ◽  
Felipe M. Martinez
Keyword(s):  
Soil Layer ◽  
Water System ◽  
Deterministic Models ◽  
Risk Models ◽  
First Order ◽  
Sensitivity Indices ◽  
Reliability Method ◽  
Input Variables ◽  
Relationship Of ◽  
The Relationship

To investigate the reliability of a sandy soil layer in an ocean wave environment a liquefaction model is used in conjunction with a first order reliability method. Thus, sensitivity indices of the soil-water system with respect to the uncertain strength and input variables are computed, and the relative importance of the various factors defining the problem can be determined. The relationship of this approach with more conventional design methods (deterministic models, risk models) is discussed along with the range of applicability of the different safety measurements.

scholarly journals Deterministic Sensitivity Analysis for First-Order Monte Carlo Simulations: A Technical Note

2009 ◽  
Vol 12 (1) ◽  
pp. 96-97 ◽  
Author(s):  
Benjamin P. Geisler ◽  
Uwe Siebert ◽  
G. Scott Gazelle ◽  
David J. Cohen ◽  
Alexander Göhler
Keyword(s):  
Sensitivity Analysis ◽  
Monte Carlo ◽  
Monte Carlo Simulations ◽  
Technical Note ◽  
First Order ◽  
Deterministic Sensitivity Analysis

Sensitivity analysis of an urban stormwater microorganism model

2010 ◽  
Vol 62 (6) ◽  
pp. 1393-1400 ◽  
Author(s):  
D. T. McCarthy ◽  
A. Deletic ◽  
V. G. Mitchell ◽  
C. Diaper
Keyword(s):  
Sensitivity Analysis ◽  
Monte Carlo ◽  
Markov Chain ◽  
Markov Chain Monte Carlo ◽  
Monte Carlo Analysis ◽  
Parameter Distribution ◽  
Model Parameters ◽  
Urban Stormwater ◽  
Urban Catchments ◽  
Two Parameters

This paper presents the sensitivity analysis of a newly developed model which predicts microorganism concentrations in urban stormwater (MOPUS—MicroOrganism Prediction in Urban Stormwater). The analysis used Escherichia coli data collected from four urban catchments in Melbourne, Australia. The MICA program (Model Independent Markov Chain Monte Carlo Analysis), used to conduct this analysis, applies a carefully constructed Markov Chain Monte Carlo procedure, based on the Metropolis-Hastings algorithm, to explore the model's posterior parameter distribution. It was determined that the majority of parameters in the MOPUS model were well defined, with the data from the MCMC procedure indicating that the parameters were largely independent. However, a sporadic correlation found between two parameters indicates that some improvements may be possible in the MOPUS model. This paper identifies the parameters which are the most important during model calibration; it was shown, for example, that parameters associated with the deposition of microorganisms in the catchment were more influential than those related to microorganism survival processes. These findings will help users calibrate the MOPUS model, and will help the model developer to improve the model, with efforts currently being made to reduce the number of model parameters, whilst also reducing the slight interaction identified.

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