Models, Uncertainty, and the Sandia V&V Challenge Problem

2020 ◽  
Vol 5 (1) ◽  
Author(s):  
George A. Hazelrigg ◽  
Georgia-Ann Klutke
Keyword(s):  
Probability Theory ◽  
Decision Theory ◽  
Uncertainty Quantification ◽  
Model Validation ◽  
Current Literature ◽  
Current Approach ◽  
Ill Posed ◽  
Solution Techniques

Abstract The purpose of this paper is not to present new results; rather, it is to show that the current approach to model validation is not consistent with the accepted mathematics of probability theory. Specifically, we argue that the Sandia V&V Challenge Problem is ill-posed in that the answers sought do not, mathematically, exist. We apply our arguments to show the types of mistakes present in the papers presented in the Journal of Verification, Validation and Uncertainty Quantification, Volume 1,1 along with the challenge problem. Further, we argue that, when the problem is properly posed, both the applicable methodology and the solution techniques are easily drawn from the well-developed mathematics of probability and decision theory. The unfortunate aspect of the challenge problem as currently stated is that it leads to incorrect and inappropriate mathematical approaches that should be avoided and corrected in the current literature.

Models, Uncertainty, and the Sandia V&V Challenge Problem

2018 ◽  
Author(s):  
George A. Hazelrigg ◽  
Georgia-Ann Klutke
Keyword(s):  
Decision Theory ◽  
Current Literature ◽  
Ill Posed ◽  
Solution Techniques

In this paper, we argue that the Sandia V&V Challenge Problem is ill-posed in that the answers sought do not, mathematically, exist. This effectively discredits both the methodologies applied to the problem and the results, regardless of the approach taken. We apply our arguments to show the types of mistakes present in the papers presented in J. of VVUQ along with the Challenge Problem. Further, we show that, when the problem is properly posed, both the applicable methodology and the solution techniques are easily drawn from the well-developed mathematics of probability and decision theory. The unfortunate aspect of the Challenge Problem as currently stated is that it leads to incorrect and inappropriate mathematical approaches that should be avoided and corrected in the current literature.

scholarly journals A Logic of Comparative Support: Qualitative Conditional Probability Relations Representable by Popper Functions

2017 ◽  
Author(s):  
James Hawthorne
Keyword(s):  
Probability Theory ◽  
Decision Theory ◽  
Classical Logic ◽  
Scientific Theory ◽  
Classical Probability ◽  
Open Questions ◽  
Classical Setting ◽  
Alternative Approaches ◽  
Popper Functions ◽  
Self Reference

Revising classical logic—to deal with the paradoxes of self-reference, or vague propositions, for the purposes of scientific theory or of metaphysical anti-realism—requires the revision of probability theory. This chapter reviews the connection between classical logic and classical probability, clarifies nonclassical logic, giving simple examples, explores modifications of probability theory, using formal analogies to the classical setting, and provides two foundational justifications for these ‘nonclassical probabilities’. There follows an examination of extensions of the nonclassical framework: to conditionalization and decision theory in particular, before a final review of open questions and alternative approaches, and an evaluation of current progress.

Experimental Assessment, Model Validation, and Uncertainty Quantification of a Pilot-Scale Gasifier

2016 ◽  
Vol 55 (25) ◽  
pp. 6961-6970 ◽  
Author(s):  
M. Hossein Sahraei ◽  
Marc A. Duchesne ◽  
Robin W. Hughes ◽  
Luis A. Ricardez-Sandoval
Keyword(s):  
Uncertainty Quantification ◽  
Model Validation ◽  
Pilot Scale ◽  
Assessment Model ◽  
Experimental Assessment

Multiscale Variability and Uncertainty Quantification Based on a Generalized Multiscale Markov Model

2010 ◽  
Author(s):  
Yan Wang
Keyword(s):  
Probability Theory ◽  
Bayesian Inference ◽  
Markov Model ◽  
Uncertainty Quantification ◽  
System Analysis ◽  
Scale Validation ◽  
Uncertainty Propagation ◽  
Bayes Rule ◽  
Imprecise Probability ◽  
Modal Extension

Variability is inherent randomness in systems, whereas uncertainty is due to lack of knowledge. In this paper, a generalized multiscale Markov (GMM) model is proposed to quantify variability and uncertainty simultaneously in multiscale system analysis. The GMM model is based on a new imprecise probability theory that has the form of generalized interval, which is a Kaucher or modal extension of classical set-based intervals to represent uncertainties. The properties of the new definitions of independence and Bayesian inference are studied. Based on a new Bayes’ rule with generalized intervals, three cross-scale validation approaches that incorporate variability and uncertainty propagation are also developed.

A Collaboration-based Approach to CFD Model Validation and Uncertainty Quantification (VUQ) Using Data from a Laminar Helium Plume

2016 ◽  
Vol 97 (2) ◽  
pp. 427-449
Author(s):  
Weston M. Eldredge ◽  
Pál Tóth ◽  
Laurie Centauri ◽  
Eric G. Eddings ◽  
Kerry E. Kelly ◽  
...  
Keyword(s):  
Uncertainty Quantification ◽  
Model Validation ◽  
Cfd Model ◽  
Using Data ◽  
Helium Plume

Randomized switching in the two-envelope problem

2009 ◽  
Vol 465 (2111) ◽  
pp. 3309-3322 ◽  
Author(s):  
Mark D. McDonnell ◽  
Derek Abbott
Keyword(s):  
Probability Theory ◽  
Decision Theory ◽  
New Approach ◽  
Switching Strategy ◽  
It Impacts ◽  
State Switching ◽  
Economics Literature ◽  
First Time ◽  
Deterministic Switching

The two-envelope problem is a conundrum in decision theory that is subject to longstanding debate. It is a counterintuitive problem of decidability between two different states, in the presence of uncertainty, where a player’s payoff must be maximized in some fashion. The problem is a significant one as it impacts on our understanding of probability theory, decision theory and optimization. It is timely to revisit this problem, as a number of related two-state switching phenomena are emerging in physics, engineering and economics literature. In this paper, we discuss this wider significance, and offer a new approach to the problem. For the first time, we analyse the problem by adopting Cover’s switching strategy—this is where we randomly switch states with a probability that is a smoothly decreasing function of the observed value of one state. Surprisingly, we show that the player’s payoff can be increased by this strategy. We also extend the problem to show that a deterministic switching strategy, based on a thresholded decision once the amount in an envelope is observed, is also workable.

scholarly journals The ambiguity dilemma in procurement projects

2019 ◽  
Vol 34 (4) ◽  
pp. 792-800 ◽  
Author(s):  
Mehdi Rajabi Asadabadi ◽  
Keiran Sharpe
Keyword(s):  
Game Theory ◽  
Decision Theory ◽  
Current Literature ◽  
Design Methodology ◽  
Imperfect Information ◽  
Rational Agency ◽  
Content Type ◽  
Procurement Process

PurposeThe purpose of this paper is to use game theory and ambiguity theory to show how “economically rational” vendors will behave in a procurement process that runs over more than one period. In light of that behavior, we have proposed “economically rational” counter-strategies on the part of purchasers.Design/methodology/approachBased on a perception–expectation framework, a unique game-based approach is designed. The authors have proposed “economically rational” counter-strategies on the part of purchasers, which are premised on the theory of rational agency.FindingsAmbiguity in the procurement process is a bane for procuring principals and a boon for suppliers – for the former, it is an issue to be managed, and for the latter it provides an opportunity to extract “insurance rents” from the principals. The authors show that, under certain conditions, the contracting principal can be exploited by a rational, rent-extracting vendor. In particular, they show that there is an incentive for a vendor to delay the resolution of ambiguities in the contract until late in the procurement process, when the insurance rents are at a maximum.Originality/valueThis study contributes to the current literature by highlighting an existing problem in the procurement process and describing it using decision theory under ambiguity in a game-like setting. Specifically, the authors use game theory in a unique way to deal with imperfect information coupled with ambiguity.

scholarly journals Research on Model Validation and Uncertainty Quantification of Airfoil Flow

2021 ◽  
Vol 1985 (1) ◽  
pp. 012015
Author(s):  
Chao Zhang ◽  
Jiangtao Chen ◽  
Jiao Zhao ◽  
Xiaojun Wu
Keyword(s):  
Uncertainty Quantification ◽  
Model Validation ◽  
Airfoil Flow
Sign in / Sign up

Export Citation Format

Share Document