Cet expose comporte deux parties: la premiere rappelle comment Ferdinand Gonseth comprenait ce terme de Referentiel qu'il avait auparavant introduit. La deuxieme s'efforcera de preciser quelque peu cette notion par une interpretation topologico-dynamique.

This article is a collection of letters solicited by the editors of the Bulletin in response to a previous article by Jaffe and Quinn [math.HO/9307227]. The authors discuss the role of rigor in mathematics and the relation between mathematics and theoretical physics.

René Thom scrute les propriétés qu’on peut assigner à tout lieu, et désigne la question de ses bords, celle des extrémités. Il s’interroge sur la théorie aristotélicienne des lieux que la transposition topologique éclaire. Des réflexions sur le lieu propre à un animal et des impressions de voyage de Marcel Proust étayent la construction.

- Biologie: fonction physiologique

This lecture is an overview of the author's own work from homotopy theory and homological algebra to the recent books Esquisse d'une Sémiophysique and Apologie du Logos, with emphasis on the rôle played by different ideas from biology in catastrophe theory.

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We consider Bayesian inference techniques for agent-based (AB) models, as an alternative to simulated minimum distance (SMD). Three computationally heavy steps are involved: (i) simulating the model, (ii) estimating the likelihood and (iii) sampling from the posterior distribution of the parameters. Computational complexity of AB models implies that efficient techniques have to be used with respect to points (ii) and (iii), possibly involving approximations. We first discuss non-parametric (kernel density) estimation of the likelihood, coupled with Markov chain Monte Carlo sampling schemes. We then turn to parametric approximations of the likelihood, which can be derived by observing the distribution of the simulation outcomes around the statistical equilibria, or by assuming a specific form for the distribution of external deviations in the data. Finally, we introduce Approximate Bayesian Computation techniques for likelihood-free estimation. These allow embedding SMD methods in a Bayesian framework, and are particularly suited when robust estimation is needed. These techniques are first tested in a simple price discovery model with one parameter, and then employed to estimate the behavioural macroeconomic model of De Grauwe (2012), with nine unknown parameters.

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