A relationship between the ordinary maximum entropy method and the method of maximum entropy in the mean

There are two entropy-based methods to deal with linear inverse problems, which we shall call the ordinary method of maximum entropy (OME) and the method of maximum entropy in the mean (MEM). Not only does MEM use OME as a stepping stone, it also allows for greater generality. First, because it allows to include convex constraints in a natural way, and second, because it allows to incorporate and to estimate (additive) measurement errors from the data. Here we shall see both methods in action in a specific example. We shall solve the discretized version of the problem by two variants of MEM and directly with OME. We shall see that OME is actually a particular instance of MEM, when the reference measure is a Poisson Measure.

• Autores: Gzyl, Henryk; ter Horst, Enrique
• Tipo de recurso: Article of investigation
• Fecha de publicación: 2014
• Institución: Colegio de Estudios Superiores de Administración
• Repositorio: Repositorio CESA
• Idioma: eng
• OAI Identifier: oai:repository.cesa.edu.co:10726/5127
• Acceso en línea: http://hdl.handle.net/10726/5127; https://doi.org/10.3390/e16021123
• Palabra clave: Maximum entropy; Maximum entropy in the mean; Constrained linear inverse problems
• Rights: openAccess
• License: Abierto (Texto Completo)