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I was going through the paper of O'Malley and Zaslavsky (2008) for the scaled inverse Wishart priors for a covariance matrix, in order to write an R-code for hierarchical Bayesian estimation of mixed logit model. They have decomposed the covariance matrix as Sigma = DeltaPhiDelta; Delta$$\Sigma = \Delta\Phi\Delta$$; $$\Delta$$ is a diagonal matrix of delta_i$$\delta_i$$ and log(delta_i)~Normal(m,s)$$\log(\delta_i) \sim \mathcal{N}(m,s)$$; Phi$$\Phi$$ is a correlation matrix, Phi~IW(nu,I)$$\Phi \sim IW(nu,I)$$.

They have used MCMC methods, combination of Gibbs sampling with Metropolis Hastings steps. In order to update the delta_i$$\delta_i$$ they used Metropolis Hasting step where the proposal distribution is the logarithm of a t distribution with 3 degrees of freedom. The details are given in the following picture:

I have defined the metropolis hasting step as But I'm not sure whether this is correct or not, as I'm getting non-positive definite covariance matrices. Should I use the proposed distribution in Metropolis Hasting or not?

I was going through the paper of O'Malley and Zaslavsky (2008) for the scaled inverse Wishart priors for a covariance matrix, in order to write an R-code for hierarchical Bayesian estimation of mixed logit model. They have decomposed the covariance matrix as Sigma = DeltaPhiDelta; Delta is a diagonal matrix of delta_i and log(delta_i)~Normal(m,s); Phi is a correlation matrix, Phi~IW(nu,I).

They have used MCMC methods, combination of Gibbs sampling with Metropolis Hastings steps. In order to update the delta_i they used Metropolis Hasting step where the proposal distribution is the logarithm of a t distribution with 3 degrees of freedom. The details are given in the following picture:

I have defined the metropolis hasting step as But I'm not sure whether this is correct or not, as I'm getting non-positive definite covariance matrices. Should I use the proposed distribution in Metropolis Hasting or not?

I was going through the paper of O'Malley and Zaslavsky (2008) for the scaled inverse Wishart priors for a covariance matrix, in order to write an R-code for hierarchical Bayesian estimation of mixed logit model. They have decomposed the covariance matrix as $$\Sigma = \Delta\Phi\Delta$$; $$\Delta$$ is a diagonal matrix of $$\delta_i$$ and $$\log(\delta_i) \sim \mathcal{N}(m,s)$$; $$\Phi$$ is a correlation matrix, $$\Phi \sim IW(nu,I)$$.

They have used MCMC methods, combination of Gibbs sampling with Metropolis Hastings steps. In order to update the $$\delta_i$$ they used Metropolis Hasting step where the proposal distribution is the logarithm of a t distribution with 3 degrees of freedom. The details are given in the following picture:

I have defined the metropolis hasting step as But I'm not sure whether this is correct or not, as I'm getting non-positive definite covariance matrices. Should I use the proposed distribution in Metropolis Hasting or not?

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What is the correct form of Metropolis Hasting step in scaled Inverse Wishart prior for covariance matrix?

I was going through the paper of O'Malley and Zaslavsky (2008) for the scaled inverse Wishart priors for a covariance matrix, in order to write an R-code for hierarchical Bayesian estimation of mixed logit model. They have decomposed the covariance matrix as Sigma = DeltaPhiDelta; Delta is a diagonal matrix of delta_i and log(delta_i)~Normal(m,s); Phi is a correlation matrix, Phi~IW(nu,I).

They have used MCMC methods, combination of Gibbs sampling with Metropolis Hastings steps. In order to update the delta_i they used Metropolis Hasting step where the proposal distribution is the logarithm of a t distribution with 3 degrees of freedom. The details are given in the following picture:

I have defined the metropolis hasting step as But I'm not sure whether this is correct or not, as I'm getting non-positive definite covariance matrices. Should I use the proposed distribution in Metropolis Hasting or not?