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

TL;DR

This note critically examines Simpson et al.'s 2017 work on penalising model component complexity, questioning the generalizability and mathematical precision of their principles in Bayesian modeling.

Contribution

It provides a critical perspective on the conceptual foundations of penalising model component complexity, highlighting uncertainties and limitations in their approach.

Findings

Questions the applicability of the principles outside specific models

Highlights the conceptual rather than mathematical nature of key notions

Expresses concerns about the extension of priors and the establishment of reference priors

Abstract

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.