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A Bayesian Dilemma

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Statistical and Fuzzy Approaches to Data Processing, with Applications to Econometrics and Other Areas

Part of the book series: Studies in Computational Intelligence ((SCI,volume 892))

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Abstract

An example is given in which a Bayesian reasoner fails to learn the obvious. That failure calls into question whether Bayesian epistemology is complete and correct as it stands.

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Notes

  1. 1.

    By “Bayesian reasoning” is meant the type of reasoning advocated by epistemic Bayesians, that is by adherents of Bayesian epistemology. (As discussed in [3], epistemic Bayesians are much different from pragmatic Bayesians.) In Bayesian epistemology, one should update one’s beliefs by conditioning them on observations. For more detailed information, see [8, Chap. 2] and [10, Chap. 4], the latter book having been reviewed by me in [2]. For a briefer, less complete account, see my paper [3].

  2. 2.

    Which we will call the Plastic-Yoking Mechanism.

  3. 3.

    Many pragmatic Bayesians would advise this [9, Chap. 6]. For a discussion of the difference between pragmatic Bayesians and epistemic Bayesians, see [3].

  4. 4.

    For explanation and discussion of the log odds ratio, also called the “log cross-product ratio”, see [5, pp. 13–18] or [4, pp. 26–28].

  5. 5.

    Philosophers of science have developed multiple theories of propensity: see [10, Chaps. 6 and 7] and [8, pp. 76–77].

  6. 6.

    An example of a simple model that describes hypothesized natural mechanisms and employs probabilistic propensities is the All-or-None Model of Paired-Associate Learning [6],  [1, Chap. 3] that I discussed in [3].

  7. 7.

    https://math.stackexchange.com/questions/122296/how-to-evaluate-this-integral-relating-to-binomial.

References

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  3. D. Bamber, Statisticians should not tell scientists what to think, in Structural Changes and Their Econometric Modeling, ed. by V. Kreinovich, S. Sriboonchitta (Proceedings of the meeting of the Thailand Econometric Society, January 2019, Chiang Mai.), pp. 63–82. Studies in Computational Intelligence, vol. 808 (Springer, Cham, Switzerland, 2019)

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  4. D. Bamber, I.R. Goodman, H.T. Nguyen, High-probability logic and inheritance, in Mathematical Models of Perception and Cognition: A Festschrift for James T. Townsend, ed. by J.W. Houpt, L.M. Blaha, vol. 1 (Psychology Press, New York, 2016), pp. 13–36

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Author information

Authors and Affiliations

  1. Cognitive Sciences Department, University of California, Irvine, USA

    Donald Bamber

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  1. Donald Bamber
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Correspondence to Donald Bamber .

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Editors and Affiliations

  1. Department of Computer Science, University of Texas at El Paso, El Paso, TX, USA

    Vladik Kreinovich

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Bamber, D. (2021). A Bayesian Dilemma. In: Kreinovich, V. (eds) Statistical and Fuzzy Approaches to Data Processing, with Applications to Econometrics and Other Areas. Studies in Computational Intelligence, vol 892. Springer, Cham. https://doi.org/10.1007/978-3-030-45619-1_2

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