分野別セミナー

通常と曜日が異なり，水曜なのでご注意下さい．

Covariance Selection Models are useful in multivariate data
analysis. They reduce the number of parameters in the inverse covariance
matrix for Gaussian data by setting some entries to zero. Decomposable
covariance selection models are special cases of covariance selection
models. Their properties allow a factorization of a probability density
for the covariance matrix called the Hyper Inverse Wishart (HIW)
distribution.
Giudici (1996) uses a Bayesian model and expressions for the marginal
likelihood to calculate the posterior probability of the decomposable
graphs. Giudici and Green (1999) give a Markov chain Monte Carlo (MCMC)
approach for decomposable models that generates the covariance matrix.
We considers similar Bayesian models to Giudici (1996) and Giudici and
Green (1999), where the corresponding graphs are decomposable. We
implement an efficient sampler by integrating the covariance matrix out
of all conditional distributions. We show that the reduced conditional
sampler is efficient, in that it converges quickly and it has low
autocorrelation function for the generated estimates of the inverse
covariance matrix.