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I am sampling covariance matrix from a Inverse Wishart distribution. In one dimensional case, after doing sufficient iterations I am taking the mode value for variance (after removing the burn-in values). How to do the same in a multivariate case?

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  • $\begingroup$ 1) Do you mean Wishart or Inverse Wishart? $\endgroup$ – Simon Byrne Dec 6 '10 at 11:07
  • $\begingroup$ 2) What do you mean by "maximum occurrence"? Are you trying to find the mode (the point of highest density)? $\endgroup$ – Simon Byrne Dec 6 '10 at 11:10
  • $\begingroup$ Sorry for being vague, I have modified the question. $\endgroup$ – Saurabh Saxena Dec 7 '10 at 4:26
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You shouldn't need a Gibbs sampler: the mode of an inverse-Wishart has a closed form.

Also, independent random samples from the Cholesky factor of a Wishart can be obtained from the Bartlett decomposition: as it is triangular, it can be inverted easily by forward subsitution to get the Cholesky factor of an inverse-Wishart.

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If I understand your question correctly:

Covariance matrix for 1-dim case reduces to the variance. Wishart Distribution (or Inv wishart distribution depending on your formulation) is a prior of covariance matrices, which for dimensions $\geq$ 2 correspond to multivariate case.

However, I may have misunderstood you. Please correct me if that is the case.

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  • $\begingroup$ You got it correctly, it is very easy to sample a variance from the distribution (by taking out the mode value). But I am not sure how to do that in multivariate case. I am using an Inverse Wishart distribution for sampling Covariance matrix. $\endgroup$ – Saurabh Saxena Dec 7 '10 at 4:31

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