Translating Predictive Distributions into Informative Priors

When complex Bayesian models exhibit implausible behavior, one solution is to assemble available information into an informative prior. Challenges arise as prior information is often only available for the observable quantity, or some model-derived marginal quantity, rather than directly pertaining to the (usually latent) parameters in our model. We propose a method for translating available prior information, in the form of an elicited distribution for the observable or model-derived marginal quantity, into an informative joint prior. Our approach proceeds given a parametric class of prior distributions with as yet undetermined hyperparameters, and minimizes the difference between the supplied elicited…

• MR
  Medical Research Council

  Awards: MC_UU_00002/2, MC_UU_00040/04, MC_UU_00002/20
• EA
  Engineering and Physical Sciences Research Council

  Award: EP/N510129/1