http://www.andreasaltelli.eu/file/repository/PUBLISHED_PAPER.pdf

Variance based sensitivity analysis of model output. Design and estimator for the total sensitivity index

Latin hypercube sampling and the propagation of uncertainty in analyses of complex systems

https://digital.library.unt.edu/ark:/67531/metadc891681/m2/1/high_res_d/886897.pdf

Survey of sampling-based methods for uncertainty and sensitivity analysis

The following techniques for uncertainty and sensitivity analysis are briefly summarized: Monte Carlo analysis, differential analysis, response surface methodology, Fourier amplitude sensitivity test, Sobol’ variance decomposition, and fast probability integration. Desirable features of Monte Carlo analysis in conjunction with Latin hypercube sampling are described in discussions of the following topics: (i) properties of random, stratified and Latin hypercube sampling, (ii) comparisons of random and Latin hypercube sampling, (iii) operations involving Latin hypercube sampling (i.e. correlation control, reweighting of samples to incorporate changed distributions, replicated sampling to test reproducibility of results), (iv) uncertainty analysis (i.e. cumulative distribution functions, complementary cumulative distribution functions, box plots), (v) sensitivity analysis (i.e. scatterplots, regression analysis, correlation analysis, rank transformations, searches for nonrandom patterns), and (vi) analyses involving stochastic (i.e. aleatory) and subjective (i.e. epistemic) uncertainty. Published by Elsevier Science Ltd.

/pdf/latin-hypercube-sampling-and-the-propagation-of-uncertainty-k6f019s9h6.pdf

Latin Hypercube Sampling and the Propagation of Uncertainty in Analyses of Complex Systems

https://pure.tue.nl/ws/files/3733415/845663329264403.pdf

Uncertainty analysis in building performance simulation for design support

There are many different ways to perform sensitivity analyses in answering these questions but they may not yield identical results. In this paper we will be concentrating on item (a) above. Many authors, when referring to the degree to which an input parameter affects the model output, use the terms ‘sensitive’, ‘important’, ‘most influential’, etc. The methods that will be discussed and used to perform SA in this paper are called ‘Variancebased methods’, in that the variability, or uncertainty, associated with an important input parameter is propagated through the model resulting in a large contribution to the overall output variability. Methods such as “importance measure” (Iman and Hora 1990, Saltelli et al. 1993, Homma and Saltelli 1996), or “correlation ratio” (Krzykacz 1990, McKay 1996), are capable of estimating the “main effect” contribution of each parameter to the output variance. However, whether a parameter is influential or not depends also on the interactions and influences of all the parameters. Derived from quite a ABSTRACT

/pdf/sensitivity-analysis-of-model-output-variance-based-methods-4lplps11pn.pdf

Sensitivity analysis of model output: variance-based methods make the difference

Sensitivity analysis aims to ascertain how each model input factor influences the variation in the model output. In performing global sensitivity analysis, we often encounter the problem of selecting the required number of runs in order to estimate the first order and/or the total indices accurately at a reasonable computational cost. The Winding Stairs sampling scheme (Jansen M.J.W., Rossing W.A.H., and Daamen R.A. 1994. In: Gasman J. and van Straten G. (Eds.), Predictability and Nonlinear Modelling in Natural Sciences and Economics. pp. 334–343.) is designed to provide an economic way to compute these indices. The main advantage of it is the multiple use of model evaluations, hence reducing the total number of model evaluations by more than half. The scheme is used in three simulation studies to compare its performance with the classic Sobol' LP_τ. Results suggest that the Jansen Winding Stairs method provides better estimates of the Total Sensitivity Indices at small sample sizes.

Winding Stairs: A sampling tool to compute sensitivity indices

The motivation of the present work is to provide an auxiliary tool for the decision-maker (DM) faced with predictive model uncertainty. The tool is especially suited for the allocation of RD or one set for the weights, and one for the factors in a multi-criteria analysis; or phenomenological parameters of the model vs. factors driving the model configuration/structure aggregation level, etc.); finally, one might imagine that a partition of the uncertainty could be sought between stochastic (or aleatory) and subjective (or epistemic) uncertainty. The present note shows how to compute rigorous decomposition of the output's variance with grouped parameters, and how this approach may be beneficial for the efficiency and transparency of the analysis.

Karen Chan

Papers

Sensitivity analysis of model output: variance-based methods make the difference

Winding Stairs: A sampling tool to compute sensitivity indices

Presenting Results from Model Based Studies to Decision-Makers: Can Sensitivity Analysis be a Defogging Agent?

Abstract sensitivity analysis of model output: variance-based methods make the differ.ence