[...]... is in fact a return A negative uncertain value of Y is what constitutes the risk This simple model could well be seen as a composite (or synthetic) indicator camp by aggregating a set of standardised base indicators Pi with weights Ci (Tarantola et al., 2002; Saisana and Tarantola, 2002) Sensitivity Analysis in Practice: A Guide to Assessing Scientific Models A Saltelli, S Tarantola, F Campolongo and... http://www.jrc.cec.eu.int/uasa/primer-SA.asp Also available at the same URL are a set of scripts in MATLAB r and the GLUEWIN software that implements a combination of global sensitivity analysis, Monte Carlo filtering and Bayesian uncertainty estimation This book is organised as follows The first chapter presents the reader with most of the main concepts of the book, through their application to a simple example, and... with applications Chapter 5 discusses variance based measures, with applications More ideas about ‘setting for the analysis are presented here Chapter 6 covers Bayesian uncertainty estimation and Monte Carlo filtering, with emphasis on the links with global sensitivity analysis Chapter 7 gives some instructions on how to use SIMLAB and, finally, Chapter 8 gives a few concepts and some opinions of various... is available The main methods that we present in this primer are all related to one another and are the method of Morris for factors’ screening and variance-based measures2 Also touched upon are Monte Carlo filtering in conjunction with either a variance based method or a simple two-sample test such as the Smirnov test All methods used in this book are model-free, in the sense that their application... giving it a name and selecting a directory A simple model 4 Go back to the left-most part of the SIMLAB main menu and click on ‘Generate’ A sample is now available for the simulation 5 We now move to the middle of the panel (Model execution) and select ‘Configure (Monte Carlo)’ and ‘Select Model’ A new panel appears 6 Select ‘Internal Model’ and ‘Create new’ A formula parser appears Enter the name... eliminate the uncertainty in one of the Px, making it into a constant, how much would this reduce the variance of Y? Beware, for unpleasant models fixing a factor might actually increase the variance instead of reducing it! It depends upon where Px is fixed 12 A worked example Chap 1 2 The problem could be: how does Vy = σ y change if one can fix a generic factor Px at its mid-point? This would be measured... 0, * for all cx (1.24) and as a result, V(E(Y|Cx)) = 0 This can also be visualised in Figure 1.3; inner conditional expectations of Y can be taken averaging along vertical ‘slices’ of the scatter plot In the case of Y vs Cs (lower panel) it is clear that such averages will form a perfectly horizontal line on the abscissas, implying a zero variance for the averaged Ys and a null sensitivity index Conversely,...x Preface Often, models use multi-dimensional uncertain parameters and/or input data to define the geographically distributed properties of a natural system In such cases, a reduced set of scalar factors has to be identified in order to characterise the multi-dimensional uncertainty in a condensed, but exhaustive fashion Factors will be sampled either from their prior distribution,... J W Jansen, a Dutch statistician, calls this latter a top marginal variance By definition the total effect measure E(V(Y|X−i )) is the expected residual output variance that one would end up with if all factors but Xi could be known or fixed Hence the term, still due to Jansen, of bottom marginal variance For the case of independent input variables, it is always true that Si ≤ STi , where the equality... from the input factor selection panel and add factors one at a time as instructed by SIMLAB Select ‘Accept factors’ when finished This takes the reader back to the ‘STATISTICAL PRE PROCESSOR’ window 3 Select a sampling method Enter ‘Random’ to start with, and ‘Specify switches’ in the right Enter something as a seed for random number generation and the number of executions (e.g 1000) Create an output .