A channel-based perspective on conjugate priors. (January 2020)

• Record Type: Journal Article
• Authors: Jacobs, B.
• Is Part Of: Mathematical structures in computer science. Volume 30:Number 1(2020)
• Page Start: 44
• Page End: 61
• Publication Date: 2020-01
• Subjects: Computer science -- Mathematics -- Periodicals; 004.015105
• DOI: 10.1017/S0960129519000082
• Languages: English
• ISSNs: 0960-1295

Abstract

Abstract: 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.