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Abstract:
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Reference prior algorithms are primarily available for models that have asymptotic posterior normality (i.e. regular cases). In recent decades, reference prior algorithms were proposed for a specific class of models whose posteriors were not asymptotically normal (i.e. non-regular cases). Despite the progress made in reference prior methodology, the existing theory lacks a unified approach for deriving reference priors. A breakthrough in unifying the reference prior theory came with Berger et al. (2009) deriving an explicit form of reference prior for single group models (i.e. models with a scalar parameter or models that have all the parameters of equal importance). Unfortunately, they couldn't generalize their approach to multi-group models. Motivated by Berger et al. (2009), we extend their main result to multi-group models. As a consequence, we derive a general expression of the conditional reference prior. We also discover that the invariance property of reference priors under specific transformations, studied by Datta and Ghosh (1996).Furthermore, we show the usefulness of our approach by computing reference priors for models that have no known reference priors.
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