Calculation of Lagrange multipliers in the construction of maximum entropy distributions in high stochastic dimension

The research addressed here concerns the construction of the probability distribution of a random vector in high dimension using the maximum entropy (MaxEnt) principle under constraints defined by the available information. In this paper, a new algorithm, adapted to the high stochastic dimension, is proposed to identify the Lagrange multipliers introduced to take into account the constraints in the MaxEnt principle. This new algorithm is based on (1) the minimization of an appropriate convex functional and (2) the construction of the probability distribution defined as the invariant measure of an Itô Stochastic Differential Equation. The methodology is validated through an application devoted to the generation of accelerograms which are physically consistent and spectrum compatible.