Inference with minimal Gibbs free energy in information field theory

Journal Article · Mon Nov 15 00:00:00 EST 2010 · Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics (Print)

DOI:https://doi.org/10.1103/PHYSREVE.82.051112· OSTI ID:21502844

Ensslin, Torsten A; Weig, Cornelius ^[1]

---

1. Max-Planck-Institut fuer Astrophysik, Karl-Schwarzschild-Str. 1, 85741 Garching (Germany)

Non-linear and non-Gaussian signal inference problems are difficult to tackle. Renormalization techniques permit us to construct good estimators for the posterior signal mean within information field theory (IFT), but the approximations and assumptions made are not very obvious. Here we introduce the simple concept of minimal Gibbs free energy to IFT, and show that previous renormalization results emerge naturally. They can be understood as being the Gaussian approximation to the full posterior probability, which has maximal cross information with it. We derive optimized estimators for three applications, to illustrate the usage of the framework: (i) reconstruction of a log-normal signal from Poissonian data with background counts and point spread function, as it is needed for gamma ray astronomy and for cosmography using photometric galaxy redshifts, (ii) inference of a Gaussian signal with unknown spectrum, and (iii) inference of a Poissonian log-normal signal with unknown spectrum, the combination of (i) and (ii). Finally we explain how Gaussian knowledge states constructed by the minimal Gibbs free energy principle at different temperatures can be combined into a more accurate surrogate of the non-Gaussian posterior.

• OSTI ID: 21502844
• Journal Information: Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics (Print), Vol. 82, Issue 5; Other Information: DOI: 10.1103/PhysRevE.82.051112; (c) 2010 The American Physical Society; ISSN 1539-3755
• Country of Publication: United States
• Language: English

Related Subjects

97 MATHEMATICAL METHODS AND COMPUTING
79 ASTROPHYSICS
COSMOLOGY AND ASTRONOMY
APPROXIMATIONS
FIELD THEORIES
FREE ENTHALPY
FUNCTIONS
GALAXIES
GAMMA ASTRONOMY
INFORMATION THEORY
NONLINEAR PROBLEMS
PROBABILITY
RED SHIFT
RENORMALIZATION
SIGNALS
SPECTRA
ASTRONOMY
CALCULATION METHODS
ENERGY
PHYSICAL PROPERTIES
THERMODYNAMIC PROPERTIES