Estimating accurate covariance matrices on fitted model parameters

Abstract

The accurate computation of the covariance matrix of fitted model parameters is a somewhat neglected task in Statistics. Algorithms are given for computing accurate covariance matrices derived from computing the Hessian matrix by numerical differentiation, and also for the covariance matrix of the posterior distribution of model parameters. Evaluations on two datasets where the Hessian could be computed analytically show that the numerical differentiation algorithm is very accurate.