A General Framework for Updating Belief Distributions

Understand

We propose a framework for general Bayesian inference.

• We argue that a valid update of a prior belief distribution to a posterior can be made for parameters which are connected to observations through a loss function rather than the traditional likelihood function, which is recovered under the special case of using self information loss.
• Modern application areas make it is increasingly challenging for Bayesians to attempt to model the true data generating mechanism.
• Moreover, when the object of interest is low dimensional, such as a mean or median, it is cumbersome to have to achieve this via a complete model for the whole data distribution.