Minimum Relative Entropy Inference for Normal and Monte Carlo Distributions

TL;DR

This paper introduces a method for inference in normal and Monte Carlo distributions using minimum relative entropy, providing analytical formulas and improved numerical techniques for partial information scenarios.

Contribution

It develops a novel representation of affine sub-manifolds of exponential families as minimum relative entropy sub-manifolds, enabling analytical and numerical inference methods.

Findings

Derived analytical formulas for inference in multivariate normal distributions.

Enhanced numerical implementation via Monte Carlo simulations.

Applicable to partial information on expectations and covariances.

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.