A question about Laplace's approximation:
In Laplace's method, we need to find the mode of a function and take second order Taylor's expansion. The first order term will vanish (since the gradient is zero at local optimum), and the second order term will be used to give a covariance of the gaussian. I am wondering if I am doing MCMC and the "point" I found is not local optimum (a.k.a gradient is not zero), will that influence my covariance matrix? Will the matrix be non-positive-definite something like that ?