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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:

enter image description here

I have defined the metropolis hasting step as enter image description here 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:

enter image description here

I have defined the metropolis hasting step as enter image description here 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:

enter image description here

I have defined the metropolis hasting step as enter image description here 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:

enter image description here

I have defined the metropolis hasting step as enter image description here 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?