Open AccessThe entropic prior for distributions with positive and negative values
Author(s) -
Hobson M. P.,
Lasenby A. N.
Publication year - 1998
Publication title -
monthly notices of the royal astronomical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.058
H-Index - 383
eISSN - 1365-2966
pISSN - 0035-8711
DOI - 10.1046/j.1365-8711.1998.01707.x
Subject(s) - physics , statistical physics , range (aeronautics) , entropy (arrow of time) , probability distribution , principle of maximum entropy , measure (data warehouse) , probability and statistics , astrophysics , statistics , quantum mechanics , mathematics , data mining , materials science , computer science , composite material
The maximum entropy method has been used to reconstruct images in a wide range of astronomical fields, but in its traditional form it is restricted to the reconstruction of strictly positive distributions. We present an extension of the standard method to include distributions that can take both positive and negative values. The method may therefore be applied to a much wider range of astronomical reconstruction problems. In particular, we derive the form of the entropy for positive/negative distributions and use direct counting arguments to find the form of the entropic prior. We also derive the measure on the space of positive/negative distributions, which allows the definition of probability integrals and hence the proper quantification of errors.