# A general framework for updating belief distributions

@article{Bissiri2013AGF, title={A general framework for updating belief distributions}, author={Pier Giovanni Bissiri and Chris C. Holmes and Stephen G. Walker}, journal={Journal of the Royal Statistical Society. Series B, Statistical Methodology}, year={2013}, volume={78}, pages={1103 - 1130} }

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 as a special case. Modern application areas make it increasingly challenging for Bayesians to attempt to model the true data‐generating mechanism. For instance, when the object of interest is low dimensional, such…

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