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A channel-based perspective on conjugate priors

Published online by Cambridge University Press:  25 February 2020

B. Jacobs
B. Jacobs*
Affiliation:
Institute for Computing and Information Sciences, Radboud University, P.O. Box 9010, 6500 GL Nijmegen, The Netherlands
*
*Email: bart@cs.ru.nl
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Abstract

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A desired closure property in Bayesian probability is that an updated posterior distribution be in the same class of distributions – say Gaussians – as the prior distribution. When the updating takes place via a statistical model, one calls the class of prior distributions the ‘conjugate priors’ of the model. This paper gives (1) an abstract formulation of this notion of conjugate prior, using channels, in a graphical language, (2) a simple abstract proof that such conjugate priors yield Bayesian inversions and (3) an extension to multiple updates. The theory is illustrated with several standard examples.

Type
Paper
Information
Mathematical Structures in Computer Science , Volume 30 , Issue 1 , January 2020 , pp. 44 - 61
Creative Commons
Creative Common License - CCCreative Common License - BY
This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted re-use, distribution, and reproduction in any medium, provided the original work is properly cited.
Copyright
© The Author(s) 2020

Footnotes

†

The research leading to these results has received funding from the European Research Council under the European Union’s Seventh Framework Programme (FP7/2007-2013)/ERC grant agreement nr. 320571.

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