Simultaneous modelling of the Cholesky decomposition of several covariance matrices

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Multivariate covariance generalized linear models (2015, methodology): “The modified Cholesky decomposition proposed by Pourahmadi et al. (2007) presents both features, but is restricted to the case where there is a natural ordering of the observations.”
Model-Based Clustering (2016, methodology): “Pourahmadi, Daniels, and Park (2007) develop a method of simultaneously modelling several covariance matrices based on this decomposition, thereby giving an alternative to common principal components analysis (Flury 1988) for longitudinal data.”
Bayesian Hierarchical Models With Conjugate Full-Conditional Distributions for Dependent Data From the Natural Exponential Family (2017, methodology): “Furthermore, the prior distributions similar to those used by Daniels and Pourahmadi (2002), Chen and Dunson (2003), and Pourahmadi et al. (2007) are adapted to the non-Gaussian setting.”
A Covariance Regression Model (2011, background): “f observations for each combination of explanatory variables may be quite small, making it impractical to estimate a separate covariance matrix for each group. One strategy, taken by Flury (1984) and Pourahmadi et al. (2007), is to assume that a particular feature of the covariance matrices (princip”