# What is the value of $\mu_0$ and $\kappa_0$in $N(\mu_0,\sigma / \kappa_0)$?

In a Bayesian analysis I want to sample $\sigma \sim \text{inverse-Wishart}(\nu_0,M)$ where $\nu_0$ is the degrees of freedom, equal to dimension+1 and $M$ is a scalar matrix

Then I will sample the $\mu$ from $\mu|\sigma \sim N(\mu_0,\sigma/\kappa_0)$. My question is, what is the value of $\mu_0$ and $\kappa_0$ and how can I determine my dimensions in the inverse-Wishart?

$\mu_0$ is the prior mean and $\kappa_0$ is the number of prior measurements, both on the $\sigma$ scale. The dimensions refer to the number of dimensions in the $d \times d$ M matrix which is also the number of dimensions/variables in the multivariate Inverse-Wishart distribution.

A basic noninformative prior distribution for the Inverse-Wishart distribution would be

$M = I = d \times d$ Identity matrix

$\nu_0 = d+1$

This gives noninformative marginal distributions, but the joint distribution is not uniform however. A noninformative $\kappa_0$ can be chosen to create a very large variance. $\mu_0$ would depend on the domain of your problem.

• @Sonayu Unfortunately, I haven't used MCMC to solve differential equations. But if there are 3 variables/parameters that you want posteriors for, then yes $d=3$ May 16, 2015 at 11:20