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Common Bayesian Models for Common Cognitive Issues

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Abstract

How can an incomplete and uncertain model of the environment be used to perceive, infer, decide and act efficiently? This is the challenge that both living and artificial cognitive systems have to face. Symbolic logic is, by its nature, unable to deal with this question. The subjectivist approach to probability is an extension to logic that is designed specifically to face this challenge. In this paper, we review a number of frequently encountered cognitive issues and cast them into a common Bayesian formalism. The concepts we review are ambiguities, fusion, multimodality, conflicts, modularity, hierarchies and loops. First, each of these concepts is introduced briefly using some examples from the neuroscience, psychophysics or robotics literature. Then, the concept is formalized using a template Bayesian model. The assumptions and common features of these models, as well as their major differences, are outlined and discussed.

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Notes

  1. From which we derive directly Bayes’ theorem, which, strictly speaking, reads P(X 2 | X 1) = P(X 1|X 2) P(X 2)/P(X 1), provided P(X 1) ≠ 0. Most of the time though, both names and equations can be used interchangeably.

  2. We note that Landy et al. (1995) did not find this type of Bayesian model to be useful.

  3. Please note that, although the notation is the same, γt refers to γ elevated to the power of t, while R t refers to R at time index t.

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Authors and Affiliations

  1. ASL, ETH Zurich, Tannenstrasse 3, 8092, Zurich, Switzerland

    Francis Colas

  2. LPNC, CNRS, UPMF, Bâtiment Sciences de l’Homme et Mathématique, BP 47, 38040, Grenoble Cedex 9, France

    Julien Diard

  3. E-Motion, LIG, CNRS, 655 avenue de l’Europe, 38334, Montbonnot Saint-Ismier, France

    Pierre Bessière

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  1. Francis Colas
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  2. Julien Diard
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Correspondence to Francis Colas.

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Colas, F., Diard, J. & Bessière, P. Common Bayesian Models for Common Cognitive Issues. Acta Biotheor 58, 191–216 (2010). https://doi.org/10.1007/s10441-010-9101-1

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