2 1 The innovative transport systems and the CityMobil project 10 1.1 The research questions 10 2 The state of art in the field of automatic transport systems 12 2.1 Case studies and demand studies for innovative transport systems 12 3 The design and implementation of surveys 14 3.1 Definition of experimental design 14 3.2 Questionnaire design and delivery 16 3.3 First analyses on the collected sample 18 4 Calibration of Logit Multionomial demand models 21 4.1 Methodology 21 4.2 Calibration of the “full” model. 22 4.3 Calibration of the “final” model 24 4.4 The demand analysis through the final Multinomial Logit model 25 5 The analysis of interaction between the demand and socioeconomic attributes 31 5.1 Methodology 31 5.2 Application of Mixed Logit models to the demand 31 5.3 Analysis of the interactions between demand and socioeconomic attributes through Mixed Logit models 32 5.4 Mixed Logit model and interaction between age and the demand for the CTS 38 5.5 Demand analysis with Mixed Logit model 39 6 Final analyses and conclusions 45 6.1 Comparison between the results of the analyses 45 6.2 Conclusions 48 6.3 Answers to the research questions and future developments 52

The European commission

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

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

This Handbook is a guide for constructing and using composite indicators for policy makers, academics, the media and other interested parties. While there are several types of composite indicators, this Handbook is concerned with those which compare and rank country performance in areas such as industrial competitiveness, sustainable development, globalization and innovation.  The Handbook aims to contribute to a better understanding of the complexity of composite indicators and to an improvement of the techniques currently used to build them.  In particular, it contains a set of technical guidelines that can help constructors of composite indicators to improve the quality of their outputs.It has been prepared jointly by the OECD (the Statistics Directorate and the Directorate for Science, Technology and Industry) and the Applied Statistics and Econometrics Unit of the Joint Research Centre (JRC) of the European Commission in Ispra, Italy.

Handbook on Constructing Composite Indicators: Methodology and User Guide

Sensitivity Analysis (SA) investigates how the variation in the output of a numerical model can be attributed to variations of its input factors. SA is increasingly being used in environmental modelling for a variety of purposes, including uncertainty assessment, model calibration and diagnostic evaluation, dominant control analysis and robust decision-making. In this paper we review the SA literature with the goal of providing: (i) a comprehensive view of SA approaches also in relation to other methodologies for model identification and application; (ii) a systematic classification of the most commonly used SA methods; (iii) practical guidelines for the application of SA. The paper aims at delivering an introduction to SA for non-specialist readers, as well as practical advice with best practice examples from the literature; and at stimulating the discussion within the community of SA developers and users regarding the setting of good practices and on defining priorities for future research. We present an overview of SA and its link to uncertainty analysis, model calibration and evaluation, robust decision-making.We provide a systematic review of existing approaches, which can support users in the choice of an SA method.We provide practical guidelines by developing a workflow for the application of SA and discuss critical choices.We give best practice examples from the literature and highlight trends and gaps for future research.

/pdf/sensitivity-analysis-of-environmental-models-4u1g2kjo5f.pdf

Sensitivity analysis of environmental models

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.

/pdf/how-to-avoid-a-perfunctory-sensitivity-analysis-1xhzjnrms8.pdf

How to avoid a perfunctory sensitivity analysis

In 1991 Morris proposed an effective screening sensitivity measure to identify the few important factors in models with many factors. The method is based on computing for each input a number of incremental ratios, namely elementary effects, which are then averaged to assess the overall importance of the input. Despite its value, the method is still rarely used and instead local analyses varying one factor at a time around a baseline point are usually employed. In this piece of work we propose a revised version of the elementary effects method, improved in terms of both the definition of the measure and the sampling strategy. In the present form the method shares many of the positive qualities of the variance-based techniques, having the advantage of a lower computational cost, as demonstrated by the analytical examples. The method is employed to assess the sensitivity of a chemical reaction model for dimethylsulphide (DMS), a gas involved in climate change. Results of the sensitivity analysis open up the ground for model reconsideration: some model components may need a more thorough modelling effort while some others may need to be simplified.

An effective screening design for sensitivity analysis of large models

The role of sensitivity analysis in ecological modelling

Sensitivity analysis provides users of mathematical and simulation models with tools to appreciate the dependency of the model output from model input and to investigate how important is each model input in determining its output. All application areas are concerned, from theoretical physics to engineering and socio-economics. This introductory paper provides the sensitivity analysis aims and objectives in order to explain the composition of the overall “Sensitivity Analysis” chapter of the Springer Handbook. It also describes the basic principles of sensitivity analysis, some classification grids to understand the application B. Iooss ( ) Industrial Risk Management Department, EDF RD biooss@yahoo.fr A. Saltelli Centre for the Study of the Sciences and the Humanities (SVT), University of Bergen (UIB), Bergen, Norway Institut de Ciencia i Tecnologia Ambientals (ICTA), Universitat Autonoma de Barcelona (UAB), Barcelona, Spain e-mail: andrea.saltelli@svt.uib.no; andrea.saltelli@jrc.ec.europa.eu © Springer International Publishing Switzerland 2015 R. Ghanem et al. (eds.), Handbook of Uncertainty Quantification, DOI 10.1007/978-3-319-11259-6_31-1 1 2 B. Iooss and A. Saltelli ranges of each method, a useful software package, and the notations used in the chapter papers. This section also offers a succinct description of sensitivity auditing, a new discipline that tests the entire inferential chain including model development, implicit assumptions, and normative issues and which is recommended when the inference provided by the model needs to feed into a regulatory or policy process. For the “Sensitivity Analysis” chapter, in addition to this introduction, eight papers have been written by around twenty practitioners from different fields of application. They cover the most widely used methods for this subject: the deterministic methods as the local sensitivity analysis, the experimental design strategies, the sampling-based and variance-based methods developed from the 1980s, and the new importance measures and metamodelbased techniques established and studied since the 2000s. In each paper, toy examples or industrial applications illustrate their relevance and usefulness.

Introduction to Sensitivity Analysis

Variance‐Based Methods

Preface. Acknowledgements. PART I: INTRODUCTION. 1 An Introduction to Credit Risk. 1.1 Credit Risk. 1.1.1 Historical and Risk-Neutral Probabilities. 1.1.2 Bond Prices and Default Probability. 1.2 Credit Risk Modelling. 1.3 Credit Derivatives. 1.4 Modelling Assumptions. 1.4.1 Probability Space and Filtrations. 1.4.2 The Risk-Free Asset. 2 An Introduction to Levy Processes. 2.1 Brownian Motion. 2.2 Levy Processes. 2.3 Examples of Levy Processes. 2.3.1 Poisson Process. 2.3.2 Compound Poisson Process. 2.3.3 The Gamma Process. 2.3.4 Inverse Gaussian Process. 2.3.5 The CMY Process. 2.3.6 The Variance Gamma Process. 2.4 Ornstein-Uhlenbeck Processes. 2.4.1 The Gamma-OU Process. 2.4.2 The Inverse Gaussian-OU Process. PART II: SINGLE-NAME MODELLING. 3 Single-Name Credit Derivatives. 3.1 Credit Default Swaps. 3.1.1 Credit Default Swaps Pricing. 3.1.2 Calibration Assumptions. 3.2 Credit Default Swap Forwards. 3.2.1 Credit Default Swap Forward Pricing. 3.3 Constant Maturity Credit Default Swaps. 3.3.1 Constant Maturity Credit Default Swaps Pricing. 3.4 Options on CDS. 4 Firm-Value Levy Models. 4.1 The Merton Model. 4.2 The Black-Cox Model with Constant Barrier. 4.3 The Levy First-Passage Model. 4.4 The Variance Gamma Model. 4.4.1 Sensitivity to the Parameters. 4.4.2 Calibration on CDS Term Structure Curve. 4.5 One-Sided Levy Default Model. 4.5.1 Wiener-Hopf Factorization and Default Probabilities. 4.5.2 Illustration of the Pricing of Credit Default Swaps. 4.6 Dynamic Spread Generator. 4.6.1 Generating Spread Paths. 4.6.2 Pricing of Options on CDSs. 4.6.3 Black's Formulas and Implied Volatility. Appendix: Solution of the PDIE. 5 IntensityLevy Models. 5.1 Intensity Models for Credit Risk. 5.1.1 Jarrow-Turnbull Model. 5.1.2 Cox Models. 5.2 The Intensity-OU Model. 5.3 Calibration of the Model on CDS Term Structures. PART III: MULTIVARIATE MODELLING. 6 Multivariate Credit Products. 6.1 CDOs. 6.2 Credit Indices. 7 Collateralized Debt Obligations. 7.1 Introduction. 7.2 The Gaussian One-Factor Model. 7.3 Generic One-Factor Levy Model. 7.4 Examples of Levy Models. 7.5 Levy Base Correlation. 7.5.1 The Concept of Base Correlation. 7.5.2 Pricing Non-Standard Tranches. 7.5.3 Correlation Mapping for Bespoke CDOs. 7.6 Delta-Hedging CDO tranches. 7.6.1 Hedging with the CDS Index. 7.6.2 Delta-Hedging with a Single-Name CDS. 7.6.3 Mezz-Equity hedging. 8 Multivariate Index Modelling. 8.1 Black's Model. 8.2 VG Credit Spread Model. 8.3 Pricing Swaptions using FFT. 8.4 Multivariate VG Model. PART IV: EXOTIC STRUCTURED CREDIT RISK PRODUCTS. 9 Credit CPPIs and CPDOs. 9.1 Introduction. 9.2 CPPIs. 9.3 Gap Risk. 9.4 CPDOs. 10 Asset-Backed Securities. 10.1 Introduction. 10.2 Default Models. 10.2.1 Generalized Logistic Default Model. 10.2.2 Levy Portfolio Default Model. 10.2.3 Normal One-Factor Default Model. 10.2.4 Generic One-Factor Levy Default Model. 10.3 Prepayment Models. 10.3.1 Constant Prepayment Model. 10.3.2 Levy Portfolio Prepayment Model. 10.3.3 Normal One-Factor Prepayment Model. 10.4 Numerical Results. Bibliography. Index.

https://www.lef.wiwi.uni-due.de/fileadmin/fileupload/BWL-LEF/Seminarreihe/0910WS/Schoutens_Slides.pdf

Jessica Cariboni

Papers

An effective screening design for sensitivity analysis of large models

The role of sensitivity analysis in ecological modelling

Introduction to Sensitivity Analysis

Variance‐Based Methods

Levy Processes in Credit Risk