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Reviews of publications on Info-Gap decision theory

Review # 7 (Posted: April 5, 2009; Last update: May 2, 2009)

Reference: Ben-Haim, Y.
Info-gap forecasting and the advantage of sub-optimal models
European Journal of Operational Research, 197, 203-213, 2009.
Abstract We consider forecasting in systems whose underlying laws are uncertain, while contextual information suggests that future system properties will differ from the past. We consider linear discrete-time systems, and use a non-probabilistic info-gap model to represent uncertainty in the future transition matrix. The forecaster desires the average forecast of a specific state variable to be within a specified interval around the correct value. Traditionally, forecasting uses a model with optimal fidelity to historical data. However, since structural changes are anticipated, this is a poor strategy. Our first theorem asserts the existence, and indicates the construction, of forecasting models with sub-optimal-fidelity to historical data which are more robust to model error than the historically optimal model. Our second theorem identifies conditions in which the probability of forecast success increases with increasing robustness to model error. The proposed methodology identifies reliable forecasting models for systems whose trajectories evolve with Knightian uncertainty for structural change over time. We consider various examples, including forecasting European Central Bank interest rates following 9/11.
Acknowledgement The author is pleased to acknowledge valuable comments and suggestions by Lior Davidovitch and Miriam Zacksenhouse.
Scores TUIGF:100%

This is a typical Info-Gap article that repeats the standard errors, misconceptions and misleading information, associated with Info-Gap decision theory. It makes no reference whatsoever to the Maximin connection thus giving the reader the false impression that the model offered here is "different". It makes no reference whatsoever to the thriving literature on Robust Optimization thus depriving the reader of the knowledge about the wider context in which it belongs. But worse than all is the absence of any discussion on the localness of Info-Gap's robustness analysis. This gives the reader a thoroughly wrong idea of the results yielded by this analysis. I should therefore point out in this regard that it is this local treatment of severe uncertainty — especially "true" Knightian uncertainty — that makes Info-Gap decision theory a classic example of a voodoo decision theory.

To enable you to see through this paper, it will be useful to simplify its notation and consider a special case of the linear model formulated in it. So consider the dynamic system

      x(t+1) = Ax(t) , t=0,1,2,3, ... , k

where t denotes time, x(t) represents the state of the process (a vector) at time t and A is the transition matrix. The value of the initial state x(0) is given. We want to find the value of the terminal state x(k+1), in fact, the m-th component of this vector, xm(k+1).

The difficulty confronting us is that the transition matrix A is unknown: its true value is subject to severe uncertainty, in fact KNIGHTIAN uncertainty. All we have is an estimate of the true value of A, call it Ã. Note that we do not index matrix A by t because Ben-Haim (2009) assumes that although the value of A is unknown, it remains constant over time.

So, given this state-of-affairs we proceed to determine the value of a matrix of the same dimensions as A, call it B, to predict the final state of the process. Our prediction will thus be given by the value of y(k+1) generated by the system

      y(t+1) = By(t) , t=0,1,2,3, ... , k

with y(0)=x(0).

The error in the prediction is then

(*)       e = y(k+1) − x(k+1) = B k+1x(0) − Ak+1x(0) = (Bk+1 − Ak+1)x(0)

observing that this is a vector and that of interest to us is the m-th component of this vector, namely em.

The question is then: what is the best choice of B, given the initial vector x(0), the estimate à of A, and the severity of the uncertainty in the true value of A?

The argument made in the paper is that even if — according to some criterion — à is the best estimate of the true value of A, it is not always the case that à is the best choice for B. But this is a hollow argument as the paper tells us nothing about how the best estimate is determined. Specifically, the paper does not proceed from the assumption that the estimate à is "best" with respect to the error of interest, namely em. Therefore, to begin with, we would have had no reason to assume that à is the best choice for B. So, what is the point of arguing that à is not always the best choice for B?

In short, the first theorem in the paper makes a trivial argument. It "shows" that subject to some technical conditions, à is not the best choice for B. And to appreciate how pointless this theorem really is, it is sufficient to point out that according to the model presented in the paper the best choice for B is defined as a value of B that maximizes the size (α) of the region of uncertainty around à subject the following performance requirement:

      |Em(B,A)| ≤ ε , ∀ A ∈ U(α,Ã)

where Em(B,A) denotes the m-th component of the error vector e generated by B and A according to (*) and U(α,Ã) denotes the region of uncertainty of size α centered at Ã.

So, what we have in Ben-Haim's (2009) theorem is a classic example of what Jan Odhnoff (1965) argues in the last paragraph of his paper (my emphasis):

It seems meaningless to draw more general conclusions from this study than those presented in section 2.2. Hence, that section maybe the conclusion of this paper. In my opinion there is room for both 'optimizing' and 'satisficing' models in business economics. Unfortunately, the difference between 'optimizing' and 'satisficing' is often referred to as a difference in the quality of a certain choice. It is a triviality that an optimal result in an optimization can be an unsatisfactory result in a satisficing model. The best things would therefore be to avoid a general use of these two words.
Jan Odhnoff
On the Techniques of Optimizing and Satisficing
The Swedish Journal of Economics
Vol. 67, No. 1 (Mar., 1965)
pp. 24-39

I fully sympathize with Odhnoff's frustration.

Who on planet Earth expects an optimal solution to Problem P to be a feasible solution — let alone an optimal solution — to Problem Q where these two problems are substantially different from each other?!?!?!?!?!

Yet, this is precisely what the paper's title — "Info-gap forecasting and the advantage of sub-optimal models" — claims to show. The paper purportedly shows, in Theorem 1, that the "best" estimate à is not the best choice — namely is sub-optimal — for B when the objective is to maximize the robustness of B according to the Info-Gap prescription.

But, given that the paper does not give us even the slightest clue about the sense in which the estimate à is "best", what exactly is the merit of Theorem 1?

This is really incredible!

Next, let us take a quick look at the robustness model set out in the paper, that is the model according to which B values are ranked. It reads as follows (+) :

      α(B,Ã) = {α ≥ 0: |Em(B,A)| ≤ ε , ∀A∈U(α,Ã)}

The larger α(B,Ã) the better. Thus, the optimal value of B is the one that maximizes the value of α(B,Ã) with respect to B.

(+) Remark: There are serious "typographical" (?) errors in the paper in the expressions defining the regions of uncertainty (eq. (5), p. 204) and the robustness model (eq. (9), p. 205).

Two observations with respect to this robustness model:

These observations apply to all Info-Gap's robustness models.

I shall not bother you with the paper's other flaws, except to call attention to one that speaks volumes about this enterprise: the paper's short, uninformative, and unrepresentative list of references.

The list of references in Ben-Haim (2009) cites no more than 7 publications — a fact that hardly enables making a case for the claim that the paper offers a new forecasting methodology. Thus, although the topic under consideration is essentially about "robust decision making in the face of severe uncertainty", there is no reference in the paper to the very important and popular area of Operations Research called Robust Optimization. Worse, no references whatsoever is made in the paper to the state of the art in decision-making under severe uncertainty. No mention whatsoever is made of how classical decision theory, operations research, and robust optimization deal with robust decision-making under severe uncertainty. Consequently, on top of there being no indication that the proposed robustness model is a Maximin model, there is no discussion whatsoever on how, why, and in what in what sense, is the robustness model proposed in the paper new or different relative to robustness models used in classical decision theory and operations research.

It is important to remember, therefore, that over the past fifty years Maximin/Minimax models have become almost synonymous with robust decision-making not only in classical decision theory but in other areas as well. For instance, here is the abstract of the entry Robust Control by Noah Williams in the New Palgrave Dictionary of Economics, Second Edition, 2008:

Robust control is an approach for confronting model uncertainty in decision making, aiming at finding decision rules which perform well across a range of alternative models. This typically leads to a minimax approach, where the robust decision rule minimizes the worst-case outcome from the possible set. This article discusses the rationale for robust decisions, the background literature in control theory, and different approaches which have been used in economics, including the most prominent approach due to Hansen and Sargent.

The following quote is from the book Robust Statistics by Huber (1981, pp. 16-17):

But as we defined robustness to mean insensitivity with regard to small deviations from assumptions, any quantitative measure of robustness must somehow be concerned with the maximum degradation of performance possible for an e-deviation from the assumptions. The optimally robust procedure minimizes this degradation and hence will be a minimax procedure of some kind.

And, of course, it is important to call attention to the refereed papers (eg. Sniedovich (2007, 2008)) outlining formal proofs that Info-Gap's robustness model is a simple Maximin model. This proof is also available at WIKIPEDIA.


Other Reviews

  1. Ben-Haim (2001, 2006): Info-Gap Decision Theory: decisions under severe uncertainty.

  2. Regan et al (2005): Robust decision-making under severe uncertainty for conservation management.

  3. Moilanen et al (2006): Planning for robust reserve networks using uncertainty analysis.

  4. Burgman (2008): Shakespeare, Wald and decision making under severe uncertainty.

  5. Ben-Haim and Demertzis (2008): Confidence in monetary policy.

  6. Hall and Harvey (2009): Decision making under severe uncertainty for flood risk management: a case study of info-gap robustness analysis.

  7. Ben-Haim (2009): Info-gap forecasting and the advantage of sub-optimal models.

  8. Yokomizo et al (2009): Managing the impact of invasive species: the value of knowing the density-impact curve.

  9. Davidovitch et al (2009): Info-gap theory and robust design of surveillance for invasive species: The case study of Barrow Island.

  10. Ben-Haim et al (2009): Do we know how to set decision thresholds for diabetes?

  11. Beresford and Thompson (2009): An info-gap approach to managing portfolios of assets with uncertain returns

  12. Ben-Haim, Dacso, Carrasco, and Rajan (2009): Heterogeneous uncertainties in cholesterol management

  13. Rout, Thompson, and McCarthy (2009): Robust decisions for declaring eradication of invasive species

  14. Ben-Haim (2010): Info-Gap Economics: An Operational Introduction

  15. Hine and Hall (2010): Information gap analysis of flood model uncertainties and regional frequency analysis

  16. Ben-Haim (2010): Interpreting Null Results from Measurements with Uncertain Correlations: An Info-Gap Approach

  17. Wintle et al. (2010): Allocating monitoring effort in the face of unknown unknowns

  18. Moffitt et al. (2010): Securing the Border from Invasives: Robust Inspections under Severe Uncertainty

  19. Yemshanov et al. (2010): Robustness of Risk Maps and Survey Networks to Knowledge Gaps About a New Invasive Pest

  20. Davidovitch and Ben-Haim (2010): Robust satisficing voting: why are uncertain voters biased towards sincerity?

  21. Schwartz et al. (2010): What Makes a Good Decision? Robust Satisficing as a Normative Standard of Rational Decision Making

  22. Arkadeb Ghosal et al. (2010): Computing Robustness of FlexRay Schedules to Uncertainties in Design Parameters

  23. Hemez et al. (2002): Info-gap robustness for the correlation of tests and simulations of a non-linear transient

  24. Hemez et al. (2003): Applying information-gap reasoning to the predictive accuracy assessment of transient dynamics simulations

  25. Hemez, F.M. and Ben-Haim, Y. (2004): Info-gap robustness for the correlation of tests and simulations of a non-linear transient

  26. Ben-Haim, Y. (2007): Frequently asked questions about info-gap decision theory

  27. Sprenger, J. (2011): The Precautionary Approach and the Role of Scientists in Environmental Decision-Making

  28. Sprenger, J. (2011): Precaution with the Precautionary Principle: How does it help in making decisions

  29. Hall et al. (2011): Robust climate policies under uncertainty: A comparison of Info-­-Gap and RDM methods

  30. Ben-Haim and Cogan (2011) : Linear bounds on an uncertain non-linear oscillator: an info-gap approach

  31. Van der Burg and Tyre (2011) : Integrating info-gap decision theory with robust population management: a case study using the Mountain Plover

  32. Hildebrandt and Knoke (2011) : Investment decisions under uncertainty --- A methodological review on forest science studies.

  33. Wintle et al. (2011) : Ecological-economic optimization of biodiversity conservation under climate change.

  34. Ranger et al. (2011) : Adaptation in the UK: a decision-making process.

Recent Articles, Working Papers, Notes

Also, see my complete list of articles
    Moshe's new book!
  • Sniedovich, M. (2012) Fooled by local robustness, Risk Analysis, in press.

  • Sniedovich, M. (2012) Black swans, new Nostradamuses, voodoo decision theories and the science of decision-making in the face of severe uncertainty, International Transactions in Operational Research, in press.

  • Sniedovich, M. (2011) A classic decision theoretic perspective on worst-case analysis, Applications of Mathematics, 56(5), 499-509.

  • Sniedovich, M. (2011) Dynamic programming: introductory concepts, in Wiley Encyclopedia of Operations Research and Management Science (EORMS), Wiley.

  • Caserta, M., Voss, S., Sniedovich, M. (2011) Applying the corridor method to a blocks relocation problem, OR Spectrum, 33(4), 815-929, 2011.

  • Sniedovich, M. (2011) Dynamic Programming: Foundations and Principles, Second Edition, Taylor & Francis.

  • Sniedovich, M. (2010) A bird's view of Info-Gap decision theory, Journal of Risk Finance, 11(3), 268-283.

  • Sniedovich M. (2009) Modeling of robustness against severe uncertainty, pp. 33- 42, Proceedings of the 10th International Symposium on Operational Research, SOR'09, Nova Gorica, Slovenia, September 23-25, 2009.

  • Sniedovich M. (2009) A Critique of Info-Gap Robustness Model. In: Martorell et al. (eds), Safety, Reliability and Risk Analysis: Theory, Methods and Applications, pp. 2071-2079, Taylor and Francis Group, London.
  • .
  • Sniedovich M. (2009) A Classical Decision Theoretic Perspective on Worst-Case Analysis, Working Paper No. MS-03-09, Department of Mathematics and Statistics, The University of Melbourne.(PDF File)

  • Caserta, M., Voss, S., Sniedovich, M. (2008) The corridor method - A general solution concept with application to the blocks relocation problem. In: A. Bruzzone, F. Longo, Y. Merkuriev, G. Mirabelli and M.A. Piera (eds.), 11th International Workshop on Harbour, Maritime and Multimodal Logistics Modeling and Simulation, DIPTEM, Genova, 89-94.

  • Sniedovich, M. (2008) FAQS about Info-Gap Decision Theory, Working Paper No. MS-12-08, Department of Mathematics and Statistics, The University of Melbourne, (PDF File)

  • Sniedovich, M. (2008) A Call for the Reassessment of the Use and Promotion of Info-Gap Decision Theory in Australia (PDF File)

  • Sniedovich, M. (2008) Info-Gap decision theory and the small applied world of environmental decision-making, Working Paper No. MS-11-08
    This is a response to comments made by Mark Burgman on my criticism of Info-Gap (PDF file )

  • Sniedovich, M. (2008) A call for the reassessment of Info-Gap decision theory, Decision Point, 24, 10.

  • Sniedovich, M. (2008) From Shakespeare to Wald: modeling wors-case analysis in the face of severe uncertainty, Decision Point, 22, 8-9.

  • Sniedovich, M. (2008) Wald's Maximin model: a treasure in disguise!, Journal of Risk Finance, 9(3), 287-291.

  • Sniedovich, M. (2008) Anatomy of a Misguided Maximin formulation of Info-Gap's Robustness Model (PDF File)
    In this paper I explain, again, the misconceptions that Info-Gap proponents seem to have regarding the relationship between Info-Gap's robustness model and Wald's Maximin model.

  • Sniedovich. M. (2008) The Mighty Maximin! (PDF File)
    This paper is dedicated to the modeling aspects of Maximin and robust optimization.

  • Sniedovich, M. (2007) The art and science of modeling decision-making under severe uncertainty, Decision Making in Manufacturing and Services, 1-2, 111-136. (PDF File) .

  • Sniedovich, M. (2007) Crystal-Clear Answers to Two FAQs about Info-Gap (PDF File)
    In this paper I examine the two fundamental flaws in Info-Gap decision theory, and the flawed attempts to shrug off my criticism of Info-Gap decision theory.

  • My reply (PDF File) to Ben-Haim's response to one of my papers. (April 22, 2007)

    This is an exciting development!

    • Ben-Haim's response confirms my assessment of Info-Gap. It is clear that Info-Gap is fundamentally flawed and therefore unsuitable for decision-making under severe uncertainty.

    • Ben-Haim is not familiar with the fundamental concept point estimate. He does not realize that a function can be a point estimate of another function.

      So when you read my papers make sure that you do not misinterpret the notion point estimate. The phrase "A is a point estimate of B" simply means that A is an element of the same topological space that B belongs to. Thus, if B is say a probability density function and A is a point estimate of B, then A is a probability density function belonging to the same (assumed) set (family) of probability density functions.

      Ben-Haim mistakenly assumes that a point estimate is a point in a Euclidean space and therefore a point estimate cannot be say a function. This is incredible!

  • A formal proof that Info-Gap is Wald's Maximin Principle in disguise. (December 31, 2006)
    This is a very short article entitled Eureka! Info-Gap is Worst Case (maximin) in Disguise! (PDF File)
    It shows that Info-Gap is not a new theory but rather a simple instance of Wald's famous Maximin Principle dating back to 1945, which in turn goes back to von Neumann's work on Maximin problems in the context of Game Theory (1928).

  • A proof that Info-Gap's uncertainty model is fundamentally flawed. (December 31, 2006)
    This is a very short article entitled The Fundamental Flaw in Info-Gap's Uncertainty Model (PDF File) .
    It shows that because Info-Gap deploys a single point estimate under severe uncertainty, there is no reason to believe that the solutions it generates are likely to be robust.

  • A math-free explanation of the flaw in Info-Gap. ( December 31, 2006)
    This is a very short article entitled The GAP in Info-Gap (PDF File) .
    It is a math-free version of the paper above. Read it if you are allergic to math.

  • A long essay entitled What's Wrong with Info-Gap? An Operations Research Perspective (PDF File) (December 31, 2006).
    This is a paper that I presented at the ASOR Recent Advances in Operations Research (PDF File) mini-conference (December 1, 2006, Melbourne, Australia).

Recent Lectures, Seminars, Presentations

If your organization is promoting Info-Gap, I suggest that you invite me for a seminar at your place. I promise to deliver a lively, informative, entertaining and convincing presentation explaining why it is not a good idea to use — let alone promote — Info-Gap as a decision-making tool.

Here is a list of relevant lectures/seminars on this topic that I gave in the last two years.

Disclaimer: This page, its contents and style, are the responsibility of the author (Moshe Sniedovich) and do not represent the views, policies or opinions of the organizations he is associated/affiliated with.

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