# Shape of parameters marginal posterior in hierarchical Bayes model

Consider a generic hierarchical Bayes model with data $$y_i\sim p(y|\theta_i)$$, dependent of parameters $$\theta_i\sim p(\theta|\phi)$$ and hyperparameters $$\phi\sim p(\phi)$$. Furthermore, assume that $$\theta$$ is multivariate normal with unknown mean and covariance, and thus $$\phi=\{\mu,\Sigma\}$$.

I have implemented in MATLAB a Gibbs sampler of the posterior distribution $$p(\theta,\phi|y)$$, but am unsure if the marginal posterior of $$\theta$$ makes sense. According to wikipedia I have decided to use a normal-inverse Wishart distribution as an hyperprior for the mean and covariance. As it can be seen in the figure below (left-side), the marginal posterior of $$\theta$$ seems to be tailed in the side lobes and uniform at the center, whereas the mean and covariance (right-side and below figure) have a clear and well-defined peak. Does these results make sense? I am still relatively new to conjugate priors and hierarchical Bayes models. Thank you in advance.