Hi Jacob,
The code that you provided for finding the standard error for laplace approximation is correct.
log_mdd_se = sqrt(sum(diag(-inv(hessian))))
where, inv(hessian) is the inverse of the Hessian matrix and diag() extracts the diagonal elements of the matrix.
To know whether the standard error of the log marginal data density computed using the Laplace approximation is correct or not, you can compare it to the standard error computed using other methods, such as Monte Carlo simulation or numerical integration. If the standard error of the log marginal data density computed using the Laplace approximation is close to the standard error computed using Monte Carlo simulation or numerical integration, then it is likely that the Laplace approximation is a good approximation of the posterior density.
Regards,
Rishav Saha
