Page 388 - Special Topic Session (STS) - Volume 3
P. 388
STS551 Zamira Hasanah Zamzuri et al.
Then, the log of the above function is maximized. The expansion of the
function is given as
3) Sampling
We want to sample from a density proportional to
{∏ ( | , −1 )} ∏ ( | , , π) . Since this is also not a
=1 0 0 =1
recognized distribution, the Metropolis-Hastings algorithm is needed. The
same technique as (1) is used for this stage. Then, we sample from the
proposal density, multivariate-t.
Let
Then, the log of the above function is maximized. The expansion of the
function is given as
4) Sampling −1
We want to sample from from a density proportional to
( −1 | , ) ∏ ( |). We can see that this function is distributed
0
=1
0
as Wishart, hence we can sample directly from the Wishart distribution
using the Gibbs sampling.
The derivation of the function is given as
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