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Bayesian Analysis of Multivariate Probit Models  Discussion on "The Art of Data Augmentation" by van Dyk and Meng
 J. Comput. Graph. Statist
, 2000
"... i;p ) 0 denote the pdimensional covariate vector of the ith observation for i = 1; :::; n: Let z i = (z i;1 ; :::; z i;q ) 0 be the vector of latent variables, i.e., the vector of real or hypothetical unobservable quantitative responses that result in observed binary 1 responses y i . The mu ..."
Abstract

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i;p ) 0 denote the pdimensional covariate vector of the ith observation for i = 1; :::; n: Let z i = (z i;1 ; :::; z i;q ) 0 be the vector of latent variables, i.e., the vector of real or hypothetical unobservable quantitative responses that result in observed binary 1 responses y i . The multivariate probit linear regression model is specified as follows. 1) The latent variables z i;1 ; :::; and z i;q follow the multivariate normal distribution with the location vector ff 0 x i and variance covariance matrix \Psi = (/ j;k ) for i = 1; :::; n; that is z i j` iid N<
Modelbased Analysis to Improve the Performance of
, 2002
"... Inference using simulation has become a dominant theme in modern statistics, whether using the bootstrap to simulate sampling distributions of statistics, Markov chain Monte Carlo to simulate posterior distributions of parameters, or multiple imputation to simulate the posterior predictive distri ..."
Abstract
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Inference using simulation has become a dominant theme in modern statistics, whether using the bootstrap to simulate sampling distributions of statistics, Markov chain Monte Carlo to simulate posterior distributions of parameters, or multiple imputation to simulate the posterior predictive distribution of missing values. Inference via simulations can, in some cases, be greatly facilitated by accompanying methods of analysis based on more traditional mathematical statistical techniques. Here we illustrate this point using one example of such technology: the analysis, based on a Markovnormal model of the stationary distribution underlying an iterative simulation, of parallel simulations before their convergence, thereby allowing a redesign of the simulation for better performance. The potential value of this approach is documented using an example involving censored data.