Uncertainty estimates
The uncertainties of model parameters are derived from the scaled diagonal elements of the mutation distribution's covariance matrix, which is calculated by the CMA evolution strategy.
The rescaling is derived from the curvature of the cost function (at its minimum) along the line of maximum variance: the maximum eigenvalue of the rescaled covariance matrix is equal to the radius of the osculating circle of the cost function (at its minimum) along the directions of the mutation ellipsoid's principal axes.
Though the rescaling is computed accurately, the mutation distribution's covariance matrix is an approximation to the inverse Hessian of the cost function at its minimum. In consequence, Especia's uncertainty estimates are approximations, too. While computed internally, the error covariance matrix of model parameters is not included with Especia's output yet.
The figure above illustrates how the initially symmetric mutation distribution of the CMA evolution strategy adapts to the elongated curvature of an objective function.