View plots of Laplace approximations of the marginal posterior densities and compare them with the marginal prior densities.
The Laplace approximation of the posterior distribution of the original parameters is based on a joint normal distribution for the transformed parameters and applying the delta method to the covariance matrix. This means that the covariance matrix of the original parameters is equal to the diagonal matrix with partial derivatives of the original parameters with respect to the transformed times the covariance matrix of the transformed parameters times the diagonal matrix with partial derivatives. The covariance matrix of the transformed parameters is the inverse Hessian at the posterior mode, taken either from the optimization routine or from a finite difference estimation.
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