On various ways of tackling incomplete information in statistics

International audienceThis short paper discusses the contributions made to the featured section on Low Quality Data. We further refine the distinction between the ontic and epistemic views of imprecise data in statistics. We also question the extent to which likelihood functions can be viewed as belief functions. Finally we comment on the data disambiguation effect of learning methods, relating it to data reconciliation problems

L'abduction en conception architecturale : une sémiose hypostatique

Cette thèse développe un modèle sémiotique de l’abduction pour représenter un processus de conception architecturale. Elle formalise ce processus par une dualisation hypostatique du rapport sémiotique entre un problème de conception, saisi en tant que signe, et la possibilité de sa matérialisation géométrique. La dualisation réintègre ce signe dans le domaine des systèmes de savoir-concevoir utilisés en conception architecturale, et par conséquent, elle génère de nouvelles solutions architecturales. L’abduction modifie les connaissances préalables engagées dans la production d’une solution (l’hypothèse) et en introduit de nouvelles. La complexité du processus de conception implique, au niveau méthodologique et à partir d’une position épistémologique constructiviste, l’intégration de la subjectivité du concepteur dans le modèle. Ainsi résulte une incertitude des interactions entre problème de conception, production de solution, concepteur et contexte. La sémiotisation de l’abduction architecturale explicite le rôle central de l’interprétation dans la création d’une solution. D’ailleurs, la dualisation s’appuie sur la théorie des possibilités pour opérationnaliser le calcul interprétatif incertain et pour valider les hypothèses générées. En retour, la gestion de la propagation de cette incertitude, dans le modèle sémiotique, facilite l’identification et la formulation des solutions, et rend possible une émergence observationnelle de la nouveauté. Le modèle développé est appliqué à un cas de transformations architecturales géométriques dans un milieu urbain fortement caractérisé.This thesis develops a semiotic model of abduction to represent a process of architectural design. It formalizes this process by the means of a hypostatic dualization, applied to the semiotic relationship between, on the one hand, a design problem, considered as a sign, and on the other, the possibility of its geometric materialization. The dualization reintegrate this sign in the domain of know-how systems used in architectural design, and consequently, it generates new architectural solutions. Abduction modifies and augments the prior knowledge involved in producing the solution (the hypothesis). From a constructivist stance and the ensuing methodological viewpoint, the complexity of the design process implies embedding the designer’s subjectivity in the model. Thus arises an uncertainty about the interactions among design problem, solution production, designer and context. Semiotizing architectural abduction reveals the central role played by interpretation in creating a solution. Besides, dualization relies on possibility theory to formalize the resulting, and uncertain, interpretation calculus, and to validate the obtained hypotheses. In return, managing the uncertainty propagation within the semiotic model, facilitates the identification and the formulation of architectural solutions and allows for an observational emergence of novelty. The developed model is applied to a case of architectural geometric transformations in a heavily characterized neighborhood

Probabilistic abduction without priors

International audienceThis paper considers the simple problem of abduction in the framework of Bayes theorem, when the prior probability of the hypothesis is not available, either because there are no statistical data to rely on, or simply because a human expert is reluctant to provide a subjective assessment of this prior probability. This abduction problem remains an open issue since a simple sensitivity analysis on the value of the unknown prior yields empty results. This paper tries to propose some criteria a solution to this problem should satisfy. It then surveys and comments on various existing or new solutions to this problem: the use of likelihood functions (as in classical statistics), the use of information principles like maximum entropy, Shapley value, maximum likelihood. Finally, we present a novel maximum likelihood solution by making use of conditional event theory. The formal setting includes de Finetti’s coherence approach, which does not exclude conditioning on contingent events with zero probability

Probabilistic abduction without priors

This paper considers the simple problem of abduction in the framework of Bayes theorem, when the prior probability of the hypothesis is not available, either because there are no statistical data to rely on, or simply because a human expert is reluctant to provide a subjective assessment of this prior probability. This abduction problem remains an open issue since a simple sensitivity analysis on the value of the unknown prior yields empty results. This paper tries to propose some criteria a solution to this problem should satisfy. It then surveys and comments on various existing or new solutions to this problem: the use of likelihood functions (as in classical statistics), the use of information principles like maximum entropy, Shapley value, maximum likelihood. The formal setting includes de Finetti’s coherence approach, which does not exclude conditioning on contingent events with zero probability. We show that the ad hoc likelihood function method, that can be reinterpreted in terms of possibility theory, is consistent with most other formal approaches. However, the maximum entropy solution is significantly different

Probabilistic Abduction Without Priors (KR 2006)

International audienceThis paper considers the simple problem of abduction in the framework of Bayes theorem, when the prior probability of the hypothesis is not available, either because there are no statistical data to rely on, or simply because a human expert is reluctant to provide a subjective assessment of this prior probability. This abduction problem remains an open issue since a simple sensitivity analysis on the value of the unknown prior yields empty results. This paper tries to propose some criteria a solution to this problem should satisfy. It then surveys and comments on various existing or new solutions to this problem: the use of likelihood functions (as in classical statistics), the use of information principles like maximum entropy, Shapley value, maximum likelihood. The formal setting includes de Finetti’s coherence approach, which does not exclude conditioning on contingent events with zero probability. We show that the ad hoc likelihood function method, that can be reinterpreted in terms of possibility theory, is consistent with most other formal approaches. However, the maximum entropy solution is significantly different, despite some formal analogies