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Some comments about "Penalising model component complexity" by Simpson et al. (2017)

This note discusses the paper "Penalising model component complexity" by Simpson et al. (2017). While we acknowledge the highly novel approach to prior construction and commend the authors for setting new-encompassing principles that will Bayesian modelling, and while we perceive the potential connection with other branches of the literature, we remain uncertain as to what extent the principles exposed in the paper can be developed outside specific models, given their lack of precision. The very notions of model component, base model, overfitting prior are for instance conceptual rather than mathematical and we thus fear the concept of penalised complexity may not further than extending first-guess priors into larger families, thus failing to establish reference priors on a novel sound ground.