Sampling from the Truncated Multivariate Normal Distribution Using a Two-stage Transformation

Dr. Gabriel Rodriguez-Yam
(Universidad Autonama de Chapingo)

Abstract:

The truncated multivariate normal distribution is often used in Bayesian modelling and many other areas of statistics. Although the Gibbs sampler is straightforward to  implement for this distribution, the standard implementation can give unsatisfactory  results due to the correlation structure in the components of the vector. In addition, the constraints may severely degrade the mixing of the chain to the point that the procedure becomes impractical. To fix this defect, Geweke (1991, 1996) proposed a transformation so that the constraints become parallel to the axes. However, the correlation structure in the covariance matrix is untreated with this transformation. Rodriguez-Yam (2003) proposed a transformation which completely resolves the correlation structure in the covariance matrix by making it diagonal, but this procedure may result in poor mixing. In this paper both problems are simultaneously addressed using two linear transformations. The 1st solves the correlation structure in the covariance matrix, and the second solves the second problem, without damaging the result of the 1st transformation.


Fecha: Lunes 24 de Marzo de 2014
Lugar: Aula 203, Edificio Anexo
Hora: 13:00 horas
Café y galletas: 12:45 horas