Interpreting statistical evidence by using imperfect models: robust adjusted likelihood functions

By R. Royall, Tsung-Shan Tsou. 2003

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Assigning a value to a power likelihood in a general Bayesian model (2017, background): “See, for example, Royall & Tsou (2003), Zhang (2006a), Zhang (2006b), Jiang & Tanner (2008), Bissiri, Holmes & Walker (2016), Walker & Hjort (2001), Watson & Holmes (2016), Miller & Dunson (2015), Grünwald & van Ommen (2014), Syring & Martin (2015), and more generally Hansen & Sargent (2008).”
Robustness of linear mixed‐effects models to violations of distributional assumptions (2020, background): “There are approaches for obtaining robust estimators for the fixed effects for cases of small sample size and for models with violated distributional assumptions (e.g. Kenward & Roger, 1997; Kenward & Roger, 2009; Royall, 1986; Royall & Tsou, 2003).”
Inconsistency of Bayesian Inference for Misspecified Linear Models, and a Proposal for Repairing It (2014, background): “While the minimum KL divergence point is often not of intrinsic interest, for some (not all) models, P̃ can be of interest for other reasons as well (Royall and Tsou, 2003): there may be associated inference tasks for which P̃ is suitable as well.”
Local model uncertainty and incomplete‐data bias (with discussion) (2005, background): “Royall and Tsou (2003) argued that parametric inference about θ is only meaningful when θINF =θINT, and this is the assumption behind their idea of the robust adjusted likelihood function.”