Toward Machine Wald

Owhadi, Houman; Scovel, Clint

doi:10.1007/978-3-319-11259-6_3-1

Cited by 6 publications

(5 citation statements)

References 136 publications

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“…Chkrebtii et al [7] calls the process of evaluating f (t n , y − tn ) with tentative y − tn to generate z n a model interrogation. From a statistical perspective, this concept of active model interrogation is similar to the sequential analysis of Wald [63,43].…”

Section: Data Generation Mechanismmentioning

confidence: 99%

A probabilistic model for the numerical solution of initial value problems

2018

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We study connections between ordinary differential equation (ODE) solvers and probabilistic regression methods in statistics. We provide a new view of probabilistic ODE solvers as active inference agents operating on stochastic differential equation models that estimate the unknown initial value problem (IVP) solution from approximate observations of the solution derivative, as provided by the ODE dynamics. Adding to this picture, we show that several multistep methods of Nordsieck form can be recasted as Kalman filtering on q-times integrated Wiener processes. Doing so provides a family of IVP solvers that return a Gaussian posterior measure, rather than a point estimate. We show that some such methods have low computational overhead, nontrivial convergence order, and that the posterior has a calibrated concentration rate. Additionally, we suggest a step size adaptation algorithm which completes the proposed method to a practically useful implementation, which we experimentally evaluate using a representative set of standard codes in the DETEST benchmark set.

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Section: Data Generation Mechanismmentioning

confidence: 99%

A probabilistic model for the numerical solution of initial value problems

2018

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“…As in Game [46,47] and Decision Theory [49], optimal strategies for such games are randomized strategies [34]. Therefore Bayesian computation emerges naturally [36,10] in the presence of incomplete information (we refer to [38,42,26,12,41,32,33,20,35,34,10,36] for a history of the correspondence between Bayesian/statistical inference, numerical analysis and algorithm design). Given these observations the fact that quantum mechanics can naturally be interpreted as Bayesian analysis with complex numbers [8,6] suggests its natural interpretation as an optimal form of computation in presence of incomplete information.…”

Section: Theory Descriptionmentioning

confidence: 99%

On testing the simulation theory

Campbell,

Owhadi,

Sauvageau

et al. 2017

Preprint

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Can the theory that reality is a simulation be tested? We investigate this question based on the assumption that if the system performing the simulation is finite (i.e. has limited resources), then to achieve low computational complexity, such a system would, as in a video game, render content (reality) only at the moment that information becomes available for observation by a player and not at the moment of detection by a machine (that would be part of the simulation and whose detection would also be part of the internal computation performed by the Virtual Reality server before rendering content to the player). Guided by this principle we describe conceptual wave/particle duality experiments aimed at testing the simulation theory.

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“…Utilized in conjunction with optimization, it leads to minimizing least favorable structural response, or maximizing the minimum buckling load of the structure due to uncertainties. Its spiritual twin is the maximin model by Abraham Wald (1902Wald ( -1950; for the intriguing paper on Wald, the interested reader can consult with a paper by Bill Casselman (2016) (see also the papers by Moshe Sniedovich (2008) on maximin principle, and by Houman Owhadi and Scovel (2017) on uncertainty quantification).…”

Section: Introductionmentioning

confidence: 99%

Review of uncertainty quantification, associated parables, and Raphael Tuvia Haftka’s contributions

Elishakoff

2021

Struct Multidisc Optim

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Two quotes, although unusual for the abstract, immediately appear to be called for in a way of describing what this paper is about; the first one is by Alfred Freudenthal (1968) in his classic paper: "… it seems absurd to strive for more and more refinement of methods of stress-analysis of the structural elements if, in order to determine the dimensions of the structural elements, its results are subsequently compared with so-called 'working stresses,' derived in a rather crude manner by dividing the values of somewhat dubious material parameters obtained in conventional material tests by still more dubious empirical numbers called 'safety factors'." His equally classic paper by Giuseppe Grandori in Meccanica 26:17-21 (1990) resonates, as it were, with the above quote, stressing: "The probabilistic approach to structural safety is today a well-established paradigm. As to the current state of this paradigm, one can notice a dissymmetry similar to that observed by Freudenthal in the traditional approach. An overwhelming part of the research effort, in fact, has been and still is devoted to estimating failure probabilities. By contrast, only sporadic research deals with the problem of choosing an acceptable risk of failure. It is true that the adoration of the probabilistic approach is in any case a progress, even in the case when acceptable risk levels are conveniently defined, because it allows us to treat different structures with homogeneous criteria. However, the concept of structural safety will not leave the 'realm of metaphysics' unless we devise a method for justifying the choice of risk acceptability levels." As we see, the first quote criticizes the deterministic approach in engineering; the other one questions the validity of a probabilistic approach. Here we are concerned with the "mother of all problems," namely how to deal with uncertainty, which methodology to choose and why and how. Hereinafter, the author's musings on uncertainty quantification are presented, via some parables. Finally, connection will be made with the philosophy adopted by late Professor Raphael Tuvia Haftka in his researches on uncertainty.

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Toward Machine Wald

Cited by 6 publications

References 136 publications

A probabilistic model for the numerical solution of initial value problems

A probabilistic model for the numerical solution of initial value problems

On testing the simulation theory

Review of uncertainty quantification, associated parables, and Raphael Tuvia Haftka’s contributions

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