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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