A New Algorithm for Simulating a Correlation Matrix Based on Parameter Expansion and Reparameterization

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MCMCglmm Course Notes (2012, methodology): “The scalar m is chosen using the method of Ovaskainen et al. (2008) so that the proportion of successful jumps is optimal, with a rate of 0.”
MCMC Estimation of Restricted Covariance Matrices (2009, methodology): “To draw the elements of a correlation matrix in MVP models, Chib and Greenberg (1998) used independence or random-walk MH chains, whereas Liu and Daniels (2006) considered a reparameterization in which a covariance matrix, drawn from an inverse Wishart distribution, is subsequently translated to a…”
Covariance Estimation: The GLM and Regularization Perspectives (2011, background): “The latter is capable of inducing uniform (−1,1) priors on the entries ρij of the correlation matrix R; see Liu and Daniels (2006).”
A method for generating realistic correlation matrices (2011, methodology): “17 For example, methods that use simulated correlation matrices include probit anal18 ysis [29, 44], shrinkage estimation [2], meta-analysis [10], multiple comparisons [23], 19 management science [32], and factor analysis [17], as well as clustering.”