European Journal of Operational Research 289 (2021) 595–610 Contents lists available at ScienceDirect European Journal of Operational Research journal homepage: www.elsevier.com/locate/ejor Decision Support Probabilistic sensitivity measures as information value Emanuele Borgonovo a,∗ , Gordon B. Hazen b , Victor Richmond R. Jose c , Elmar Plischke d a Bocconi University and BIDSA, Milan, Italy b Northwestern University, Evanston, IL, USA c Georgetown University, Washington, DC, USA d Clausthal University of Technology, Clausthal-Zellerfeld, Germany a r t i c l e i n f o Article history: Received 12 November 2019 Accepted 6 July 2020 Available online 12 July 2020 Keywords: Decision support systems Information value Probabilistic sensitivity analysis Renyi’s postulates a b s t r a c t Decision makers increasingly rely on forecasts or predictions generated by quantitative models. Best prac- tices recommend that a forecast report be accompanied by a sensitivity analysis. A wide variety of prob- abilistic sensitivity measures have been suggested; however, model inputs may be ranked differently by different sensitivity measures. Is there some way to reduce this disparity by identifying what probabilis- tic sensitivity measures are most appropriate for a given reporting context? We address this question by postulating that importance rankings of model inputs generated by a sensitivity measure should corre- spond to the information value for those inputs in the problem of constructing an optimal report based on some proper scoring rule. While some sensitivity measures have already been identified as informa- tion value under proper scoring rules, we identify others and provide some generalizations. We address the general question of when a sensitivity measure has this property, presenting necessary and sufficient conditions. We directly examine whether sensitivity measures retain important properties such as trans- formation invariance and compliance with Renyi’s Postulate D for measures of statistical dependence. These results provide a means for selecting the most appropriate sensitivity measures for a particular reporting context and provide the analyst reasonable justifications for that selection. We illustrate these ideas using a large scale probabilistic safety assessment case study used to support decision making in the design and planning of a lunar space mission. © 2020 Elsevier B.V. All rights reserved. 1. Introduction Forecasts or predictions generated by quantitative models support decision makers in areas ranging from business planning (Baucells & Borgonovo, 2013) to climate change modeling (Stehfest et al., 2019). Frequently, these models are built to estimate a key quantity of interest (Y), which is one of the inputs to a panel where representative agents conduct the decision making process follow- ing a pre-established protocol (French & Argyris, 2018). The analyst who develops or implements the simulation is expected to provide a forecast of Y, which can be a point estimate, a quantile, or a cu- mulative distribution function of Y. Best practices recommend that such a report be accompanied by a sensitivity analysis that pro- vides a description of the level of uncertainty in the forecast and that identifies what model inputs are the drivers of the forecast, and are therefore candidates for additional information acquisition. ∗ Corresponding author. E-mail addresses: emanuele.borgonovo@unibocconi.it (E. Borgonovo), gbh305@northwestern.edu (G.B. Hazen), vrj2@georgetown.edu (V.R.R. Jose), elmar.plischke@tu-clausthal.de (E. Plischke). Common approaches to sensitivity analysis study the determin- istic variation of the quantity of interest about a base value or best estimate. This type of analysis is at the basis of popular tools such as tornado diagrams (Howard, 1988) or spider plots (Eschenbach, 1992). Analysts also have the option of assigning probability distri- butions to uncertain model inputs, and of using these distributions to construct numerical measures of sensitivity, which we synony- mously refer to as probabilistic or probabilistic sensitivity measures. However, the analyst may find a variety of such sensitivity mea- sures to use, e.g., variance-based, (Saltelli & Tarantola, 2002; Wagner, 1995), quantile-based (Browne, Fort, Iooss, & Le Gratiet, 2017), distribution-based (Gamboa, Klein, & Lagnoux, 2018), and some authors (Felli & Hazen, 1998; 1999; Oakley, 2009; Strong, Oakley, & Brennan, 2014) advocate the use of value of information. The very variety of available sensitivity measures could be a stumbling block for the analyst: Which is the right one to use? One of the difficulties associated with complex decision making problems is that analysts may be required to work in contexts in which there is no specified objective function or set of alternatives, perhaps due to a decision having already been made (Eschenbach, 1992). In these cases, because there is no explicit comparison of https://doi.org/10.1016/j.ejor.2020.07.010 0377-2217/© 2020 Elsevier B.V. All rights reserved.