A Bayesian Baseline for Belief in Uncommon Events

Authors

DOI:

https://doi.org/10.24204/ejpr.v9i3.1909

Keywords:

uncommon events, black swan, bayesian analysis, miracles

Abstract

The plausibility of uncommon events and miracles based on testimony of such an event has been much discussed. When analyzing the probabilities involved, it has mostly been assumed that the common events can be taken as data in the calculations. However, we usually have only testimonies for the common events. While this difference does not have a significant effect on the inductive part of the inference, it has a large influence on how one should view the reliability of testimonies. In this work, a full Bayesian solution is given for the more realistic case, where one has a large number of testimonies for a common event and one testimony for an uncommon event. A free-running parameter is given for the unreliability of testimony, to be determined from data. It is seen that, in order for there to be a large amount of testimonies for a common event, the testimonies will probably be quite reliable. For this reason, because the testimonies are quite reliable based on the testimonies for the common events, the probability for the uncommon event, given a testimony for it, is also higher. Perhaps surprisingly, in the simple case, the increase in plausibility from testimony for the uncommon events is of the same magnitude as the decrease in plausibility from induction. In summary, one should be more open-minded when considering the plausibility of uncommon events.

Author Biography

Vesa Palonen, University of Helsinki

Department of Physics, post-doc researcher

References

Ahmed, Arif. 2015. “Hume and the Independent Witnesses.” Mind 124 (496): 1013–44. doi:10.1093/mind/fzv076.

Earman, john. 2000. Hume’s Abject Failure : The Argument Against Miracles. Oxford University Press, USA.

Gelman, Andrew, John B Carlin, Hal S Stern, and Donald B Rubin. 2003. Bayesian Data Analysis, Second Edition. Boca Raton: Chapman & Hall/CRC.

Hume, David. 1748. An Enquiry Concerning Human Understanding. London: A. Millar. https://ebooks.adelaide.edu.au/h/hume/david/h92e/.

Millican, Peter. 2013. “Earman on Hume on Miracles.” In Debates in Modern Philosophy: Essential Readings and Contemporary Responses, edited by Stewart Duncan and Antonia LoLordo. Routledge.

Neapolitan, Richard E. 2004. Learning Bayesian Networks. Pearson Prentice Hall.

Pearl, Judea. 1997. “Bayesian Networks.” UCLA Computer Science Department, Technical Report R246: 1–5.

Shechtman, D., I. Blech, D. Gratias, and J. W. Cahn. 1984. “Metallic Phase with Long-Range Orientational Order and No Translational Symmetry.” Physical Review Letters 53 (20): 1951–53. doi:10.1103/PhysRevLett.53.1951.

Shechtman, Daniel. 2013. “Quasi-Periodic Crystals-the Long Road from Discovery to Acceptance.” Rambam Maimonides Medical Journal 4 (1). Rambam Health Care Campus: e0002. doi:10.5041/RMMJ.10102.

Sivia, D S. 1996. Data Analysis - A Bayesian Tutorial. Oxford: Clarendon Press.

Taleb, Nassim Nicholas. 2007. The Black Swan : The Impact of the Highly Improbable. Penguin Books Ltd. doi:10.5465/AMP.2011.61020810.

Downloads

Published

2017-09-21

How to Cite

Palonen, Vesa. 2017. “A Bayesian Baseline for Belief in Uncommon Events”. European Journal for Philosophy of Religion 9 (3):159-75. https://doi.org/10.24204/ejpr.v9i3.1909.