Bayesian composite marginal likelihoods

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Bayesian Inference from Composite Likelihoods, with an Application to Spatial Extremes (2009, methodology): “In their investigation of the asymptotic distribution of the the magnitude-adjusted posterior, Pauli et al. [2011, page 8] state that the posterior has approximately the correct variance “by the χ 2 approximation for the null distribution.””
Bayesian estimation of rainfall intensity-duration-frequency relationships (2015, methodology): “In this paper, we adjust the independence likelihood for appropriate inference, an idea which has been based on recent advances in Bayesian inference from composite likelihoods (Pauli et al., 2011; Ribatet et al., 2012).”
Bayesian Few-Shot Classification with One-vs-Each Pólya-Gamma Augmented Gaussian Processes (2020, background): “Prior work on Bayesian inference with composite likelihoods has shown that the composite posterior is consistent under fairly general conditions for correctly specified models (Miller, 2019) but can produce overly concentrated posteriors (Pauli et al., 2011; Ribatet et al., 2012) since each componen”