Modeling covariance matrices in terms of standard deviations and correlations, with application to shrinkage

By J. Barnard, Robert E. McCulloch, Xiao-Li Meng. 2000

717 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/d922535f117db63b46ff9d09421ecd0e277d873b

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

Citations in the corpus

Bayesian Measures of Explained Variance and Pooling in Multilevel (Hierarchical) Models (2006, unknown): “We use standard noninformative normal priors for γ0, γ1, δ0, and δ1 and noninformative uniform priors for σα, σβ , and ρ, as recommended by Barnard, McCulloch, and Meng (2000) .”
Comparison of Inverse Wishart and Separation-Strategy Priors for Bayesian Estimation of Covariance Parameter Matrix in Growth Curve Analysis (2016, methodology): “Barnard et al. (2000) introduced a separation strategy to decompose a covariance matrix into a diagonal matrix S of standard deviations and a correlation matrix R, such that = SRS, where S = (sij) with sij = 0 only if i = j and the diagonal element sii is the standard deviation of the ith variable.”
A Model for Teacher Effects From Longitudinal Data Without Assuming Vertical Scaling (2010, unknown): “Barnard et al. (2000) present an alternative to this prior.”
MCMCglmm Course Notes (2012, methodology): “I use the prior specification in Barnard et al. (2000) where nu controls how much the correlation matrix approaches an identity matrix.”
A Hierarchical Ornstein–Uhlenbeck Model for Continuous Repeated Measurement Data (2009, unknown): “One possible alternative is to decompose the covariance matrix ( Barnard, McCulloch, & Meng, 2000 ), usually into standard deviations and correlation matrices and assume proper distributions for these in order to ensure the positive definiteness.”
A New Algorithm for Simulating a Correlation Matrix Based on Parameter Expansion and Reparameterization (2006, methodology): “Note that (3.2) is the joint uniform prior defined by Barnard, McCulloch, and Meng (2000).”
MCMC Estimation of Restricted Covariance Matrices (2009, methodology): “…of a correlation matrix has been implemented in Gaussian copula models by Pitt, Chan, and Kohn (2006) using the parameterization of Wong, Carter, and Kohn (2003), and in hierarchical shrinkage models by Barnard, McCulloch, and Meng (2000) using the griddy Gibbs sampler (Ritter and Tanner 1992).”
Penalising Model Component Complexity: A Principled, Practical Approach to Constructing Priors (2014, methodology): “Along a different tack, Barnard et al. (2000) parameterise the covariance as Σ = D1/2RD1/2, where D is a diagonal matrix of marginal variances and R is a correlation matrix, that is a symmetric positive definite matrix with ones on the diagonal.”
A Bayesian analysis of the multinomial probit model with fully identified parameters (2000, methodology): “Other possible approaches to assessing priors directly on the identi"ed parameters include using the prior of Barnard et al., 2000 (see, also, in McCulloch and Rossi, 1996) and the approach of Chib et al. (1998). In the Barnard et al.”
Modelling dependence using skew t copulas: Bayesian inference and applications (2012, unknown): “(2006) and Wong, Carter & Kohn (2003), while Barnard et al. (2000) and Danaher & Smith (2009) provide sampling methods for their priors for Γ.”
Prior distributions for variance parameters in hierarchical models (comment on article by Browne and Draper) (2004, unknown): “Noninformative or weakly informative conditionally-conjugate priors could be applied to structured models such as described by Barnard, McCulloch, and Meng (2000) and Daniels and Kass (1999, 2001), expanded using multiplicative parameters as in Liu (2001) to give the models more flexibility.”