We study holonomic gradient decent for maximum likelihood estimation of exponentialpolynomial distribution, whose density is the exponential function of a polynomial in the random variable. We first consider the case that the support of the distribution is the set of positive reals. We show that the maximum likelihood estimate (MLE) can be easily computed by the holonomic gradient descent, even...

Abstract We discuss a pointwise numerical differentiation formula on multivariate scattered data, based the coefficients of local polynomial interpolation at Discrete Leja Points, written in Taylor’s monomial basis. Error bounds for approximation partial derivatives any order compatible with function regularity are provided, as well sensitivity estimates to functional perturbations, terms inver...

A priori and a posteriori error estimates are derived for the numerical approximation of scalar and complex valued phase field models. Particular attention is devoted to the dependence of the estimates on a small parameter and to the validity of the estimates in the presence of topological changes in the solution that represents singular points in the evolution. For typical singularities the es...