Default priors for Bayesian and frequentist inference

Summary. We investigate the choice of default priors for use with likelihood for Bayesian and frequentist inference. Such a prior is a density or relative density that weights an observed likelihood function, leading to the elimination of parameters that are not of interest and then a density‐type assessment for a parameter of interest. For independent responses from a continuous model, we develop a prior for the full parameter that is closely linked to the original Bayes approach and provides an extension of the right invariant measure to general contexts. We then develop a modified prior that is targeted on a component parameter of interest and by targeting avoids the marginalization paradoxes of Dawid and co‐workers. This modifies Jeffreys's prior and provides extensions to the development of Welch and Peers. These two approaches are combined to explore priors for a vector parameter of interest in the presence of a vector nuisance parameter. Examples are given to illustrate the computation of the priors.