| dc.creator |
MASSAM, HELENE |
|
| dc.creator |
Atay-Kayis, Aliye |
|
| dc.date |
2005-05-31T21:00:00Z |
|
| dc.date.accessioned |
2020-10-06T09:18:11Z |
|
| dc.date.available |
2020-10-06T09:18:11Z |
|
| dc.identifier |
04dd7a78-2a90-458a-9112-1d4cd38bcf45 |
|
| dc.identifier |
10.1093/biomet/92.2.317 |
|
| dc.identifier |
https://avesis.sdu.edu.tr/publication/details/04dd7a78-2a90-458a-9112-1d4cd38bcf45/oai |
|
| dc.identifier.uri |
http://acikerisim.sdu.edu.tr/xmlui/handle/123456789/52311 |
|
| dc.description |
A centred Gaussian model that is Markov with respect to an undirected graph G is characterised by the parameter set of its precision matrices which is the cone M+(G) of positive definite matrices with entries corresponding to the missing edges of G constrained to be equal to zero. In a Bayesian framework, the conjugate family for the precision parameter is the distribution with Wishart density with respect to the Lebesgue measure restricted to M+(G). We call this distribution the G-Wishart. When G is nondecomposable, the normalising constant of the G-Wishart cannot be computed in closed form. In this paper, we give a simple Monte Carlo method for computing this normalising constant. The main feature of our method is that the sampling distribution is exact and consists of a product of independent univariate standard normal and chi-squared distributions that can be read off the graph G. Computing this normalising constant is necessary for obtaining the posterior distribution of G or the marginal likelihood of the corresponding graphical Gaussian model. Our method also gives a way of sampling from the posterior distribution of the precision matrix. |
|
| dc.language |
eng |
|
| dc.rights |
info:eu-repo/semantics/closedAccess |
|
| dc.title |
Monte Carlo method for computing the marginal likelihood in nondecomposable Gaussian graphical models |
|
| dc.type |
info:eu-repo/semantics/article |
|