Info-Gap Modelling: Why More is Less
Yakov Ben‐Haim, Yitzhak Moda, Miriam Zacksenhouse, Anna Yofie · 2008
Non-deterministic Methods in Applied Mechanics and Engineering Leuven, Belgium, March 31 { April 02, 2008 Gauss and Legendre independently invented the method of least squares for modelling planetary orbits based on noisy astronomical data. Since then, least squares, maximum likelihood, maximum entropy and other optimization criteria have become methodological pillars for empirically modelling complex systems. In this paper will argue that these optimization techniques are adequate when the only challenge is noise in the data whose stochastic properties are known. However, when the probabilistic model is imprecisely known, or when the underlying processes are incompletely understood, then one needs a strategy which balances between fldelity to the data on the one hand, against immunity to gaps in our understanding on the other. We use info-gap decision theory to formulate such a strategy, based on the concept of robust-satisflcing. We show that models which are optimal based on the best (but uncertain) understanding, have minimal robustness against errors in that understanding. Sub-optimal models have greater robustness. Fidelity to data and understanding tradesofi against robustness to errors. This explains why \more is less when modelling complex poorly understood systems. We apply the theory to linear regression with info-gap-uncertain data. We discuss the relation between robust-satisflcing and min-maxing. References