We exhibit a strong link between frequentist PAC-Bayesian risk bounds and the Bayesian marginal likelihood. That is, for the negative log-likelihood loss function, we show that the minimization of PAC-Bayesian generalization risk bounds maximizes the Bayesian marginal likelihood. This provides an alternative explanation to the Bayesian Occam’s razor criteria, under the assumption that the data ...

Bayesian theory [5] is one of the most commonly utilized theories for managing uncertainty in information fusion [20, 12]. The theory relies on two main assumptions: (1) a probability function should be used for representing belief and (2) Bayes’ theorem should be used for belief updating when a new observation has been made. The main criticism of Bayesian theory that can be found in the litera...

Focussed Bayesian fusion reduces high computational costs caused by Bayesian fusion by restricting the range of the Properties of Interest which specify the structure of the desired information on its most task relevant part. Within this publication, it is concisely explained how Bayesian theory and the theory of statistical evidence can be combined to derive meaningful focussed Bayesian models...