Minimum Relative Entropy Inference for Normal and Monte Carlo Distributions

Abstract

We represent affine sub-manifolds of exponential family distributions as minimum relative entropy sub-manifolds. With such representation we derive analytical formulas for the inference from partial information on expectations and covariances of multivariate normal distributions; and we improve the numerical implementation via Monte Carlo simulations for the inference from partial information of generalized expectation type.

Keywords: Minimum Relative Entropy, Kullback-Leibler, Hamiltonian Monte Carlo, Flexible Probabilities, Exponential-Family Distributions

JEL Classification: C1, G11