Vinecop.hessian

Vinecop.hessian(self, u: numpy.ndarray, step_wise: bool = True, num_threads: int = 1) → numpy.ndarray

Evaluates the averaged Hessian of the log-likelihood.

Hessian is meant loosely as “gradients of each component of the score function”. The Hessian is averaged over all samples in u, yielding an \(\mathrm{npars} \times \mathrm{npars}\)matrix (use hessian_full() for the per-observation decomposition).

Parameters:

undarray, shape (n, m), dtype float

An \(n \times (d + k)\)or \(n \times 2d\)matrix of evaluation points, where \(k\)is the number of discrete variables (see select()).

step_wisebool

if False, full gradient of the log-likelihood; if True, score function of the step-wise MLE (gradients computed per pair-copula).

num_threadsint

The number of threads to use for computations; if greater than 1, the function will be applied concurrently to num_threads batches of u.