Statistics

Info-gap theory is highly suited to deal with estimation and inference under severe uncertainty. Several applications have been developed in which info-gap theory augments statistical methods by dealing with non-random uncertainty.

  • Yakov Ben-Haim, 2006, Info-Gap Decision Theory: Decisions Under Severe Uncertainty, 2nd edition, Academic Press, London.
    Section 3.2.13: Estimating an uncertain probability density.
  • Yakov Ben-Haim, 2010, Info-Gap Economics: An Operational Introduction, Palgrave-Macmillan.
    Chapter 6: Estimation and Forecasting:
    Section 6.1: Regression prediction.
    Section 6.2: Auto-regression and data revision.
    Section 6.3: Confidence intervals.
  • Yakov Ben-Haim and Mike Smithson, 2018, Data-Based Prediction under Uncertainty: A Dual Approach. Journal of Mathematical Psychology, 87: 11-30. Free access here until 14 Nov 2018. Abstract.
  • Yakov Ben-Haim, Miriam Zacksenhouse, Ronit Eshel, Raphael Levi, Avi Fuerst and Wayne Bentley, 2014, Failure detection with likelihood ratio tests and uncertain probabilities: An info-gap application, Mechanical Systems and Signal Processing, vol. 48, pp.1-14. Pre-print.
  • Yakov Ben-Haim, 2011, Interpreting null results from measurements with uncertain correlations: An info-gap approach, Risk Analysis-An International Journal, vol.31 (1), pp.78-85. Pre-print.
  • Yakov Ben-Haim and Francois Hemez, 2012, Robustness, Fidelity and Prediction-Looseness of Models,Proceedings of the Royal Society, A, 468: 227-244. Pre-print.
  • Tania Mirer and Yakov Ben-Haim, 2010, Reliability Assessment of Explosive Material Based on Penalty Tests: An Info-Gap Approach, Proceedings of the Institution of Mechanical Engineers, Part O, Journal of Risk and Reliability, vol. 224(4), pp.346-355. Pre-print.
    Abstract

    Abstract

    A method is developed for experimental assessment of reliability of a system with a stringent safety requirement: explosive material. The focus is on analysis and management of both statistical variability of measurements and non-probabilistic uncertainty in probability distributions (distributional uncertainty). Info-gap theory is used to model the distributional uncertainty in the pdf of the threshold for actuation of the explosive material. The quantitative analysis and the qualitative judgments which accompany the certification of safety are studied. A proposition is proven asserting that the info-gap robustness function, for the class of problems examined, is independent of the experimental design over virtually all of its range.

  • Yakov Ben-Haim, 2009, Info-gap forecasting and the advantage of sub-optimal models, European Journal of Operational Research, 197: 203-213. pdf file. EJOR.
  • David R. Fox, Yakov Ben-Haim, Keith R. Hayes, Michael McCarthy, Brendan Wintle, Piers Dunstan, 2007, An info-gap approach to power and sample size calculations, Environmetrics, vol. 18, pp.189-203. Pre-print.
  • Miriam Zacksenhouse, Simona Nemets, Miikhail A Lebedev and Miguel A Nicolelis, 2009, Robust Satisficing Linear Regression: performance/robustness trade-off and consistency criterion, Mechanical Systems and Signal Processing, vol. 23, pp.1954-1964,
    Abstract

    Abstract

    Linear regression quantifies the linear relationship between paired sets of input and output observations. The well known least-squares regression optimizes the performance criterion defined by the residual error, but is highly sensitive to uncertainties or perturbations in the observations. Robust least-squares algorithms have been developed to optimize the worst case performance for a given limit on the level of uncertainty, but they are applicable only when that limit is known. Herein, we present a robust-satisficing approach that maximizes the robustness to uncertainties in the observations, while satisficing a critical sub-optimal level of performance. The method emphasizes the trade-off between performance and robustness, which are inversely correlated. To resolve the resulting trade-off we introduce a new criterion, which assesses the consistency between the observations and the linear model. The proposed criterion determines a unique robust-satisficing regression and reveals the underlying level of uncertainty in the observations with only weak assumptions. These algorithms are demonstrated for the challenging application of linear regression to neural decoding for brain-machine interfaces. The model-consistent robust-satisfying regression provides superior performance for new observations under both similar and different conditions. Keywords: Linear regression, Robust regression, Regularization, Information-gap, Uncertainties, Brain machine interface.

  • Miriam Zacksenhouse, Simona Nemets, Anna Yoffe, Yakov Ben-Haim, Mikhail Lebedev, Miguel Nicolelis, An info-gap approach to linear regression, IEEE International conference on Acoustics, Speech and Signal Processing, ICASSP 2006, May 14-19, 2006, Toulouse, France, Vol.3, pp.800-803.
  • Miriam Zacksenhouse and Simona Nemets, 2011 Info-gap approach to regression,  ICVRAM 2011: 1st International Conference on Vulnerability and Risk Assessment and Management, April 11-13, 2011, University of Maryland, College Park, pp.980-987.
    Abstract

    Abstract

    The problem of determining the coefficients of a linear model from experimental data has been the subject of scientific research since the beginning of the 19th century. The standard technique, which minimizes the residual error, is sensitive to uncertainties and becomes ill-posed when the data is redundant. Regularization techniques replace the original ill-posed problem with a well-posed problem, but are sensitive to the proper selection of the regularization parameter, which controls the fidelity to the original problem. We have recently applied info-gap techniques to derive a robust-satisficing linear regression. The method is based on satisficing a level of residual error that is consistent with the data. Here we demonstrate the performance of this method and compare it to existing regularization methods including L-curve and generalized cross-validation. It is shown that the proposed method yields superior results in the presence of (i) significant noise, (ii) correlated noise, and (iii) model uncertainties.

    Copyright © ASCE 2011.

  • Carmit Keren, 2009, Info-Gap Bayesian Classification, MSc Thesis, Technion-Israel Institute of Technology. In English.
  • Ferson, S. and W.T. Tucker, 2008, Probability boxes as info-gap models, Annual Conference of the North American Fuzzy Information Processing Society – NAFIPS 2008, Article number 4531314.
  • Berleant, D., Villaverde, K. and Koseheleva, O.M., 2008, Towards a more realistic representation of uncertainty: An approach motivated by Info-Gap Decision Theory, Annual Conference of the North American Fuzzy Information Processing Society – NAFIPS 2008, Article number 4531297.
  • Matthias C.M. Troffeas and John Paul Gosling, 2012, Robust detection of exotic infectious diseases in animal herds: A comparative study of three decision methodologies under severe uncertainty, Intl J of Approximate Reasoning, 53: 1271-1281.
    Abstract

    Abstract

    When animals are transported and pass through customs, some of them may have dangerous infectious diseases. Typically, due to the cost of testing, not all animals are tested: a reasonable selection must be made. How to test effectively whilst avoiding costly disease outbreaks? First, we extend a model proposed in the literature for the detection of invasive species to suit our purpose, and we discuss the main sources of model uncertainty, many of which are hard to quantify. Secondly, we explore and compare three decision methodologies on the problem at hand, namely, Bayesian statistics, info-gap theory and imprecise probability theory, all of which are designed to handle severe uncertainty. We show that, under rather general conditions, every info-gap solution is maximal with respect to a suitably chosen imprecise probability model, and that therefore, perhaps surprisingly, the set of maximal options can be inferred at least partly – and sometimes entirely – from an info-gap analysis.

    Keywords

    Exotic disease, Lower prevision, Info-gap, Maximality, Minimax, Robustness

  • Matthias C.M. Troffeas and John Paul Gosling, Robust detection of exotic infectious diseases in animal herds: A comparative study of two decision methodologies under severe uncertainty, 7th International Symposium on Imprecise Probability: Theories and Applications, Innsbruck, Austria, 25-28 July 2011. Paper.
  • Yakov Ben-Haim, Two for the Price of One: Info-Gap Robustness of the 1-Test Algorithm, 7th International Symposium on Imprecise Probability: Theories and Applications, Innsbruck, Austria, 25-28 July 2011. Paper.
  • Yakov Ben-Haim, Tests of the Mean with Distributional Uncertainty: An Info-Gap Approach, 6th International Symposium on Imprecise Probability: Theories and Applications, Durham, United Kingdom, 14-18 July 2009.

Questions or comments on info-gap theory? Contact me at yakov@technion.ac.il