Bayesian Reconstruction of Approximately Periodic Potentials at Finite Temperature

Abstract

The paper discusses the reconstruction of potentials for quantum systems at finite temperatures from observational data. A nonparametric approach is developed, based on the framework of Bayesian statistics, to solve such inverse problems. Besides the specific model of quantum statistics giving the probability of observational data, a Bayesian approach is essentially based on "a priori" information available for the potential. Different possibilities to implement "a priori" information are discussed in detail, including hyperparameters, hyperfields, and non--Gaussian auxiliary fields. Special emphasis is put on the reconstruction of potentials with approximate periodicity. The feasibility of the approach is demonstrated for a numerical model.

18 pages, 17 figures, LaTeX

References in corpus (5)

• Monte Carlo Implementation of Gaussian Process Models for Bayesian Regression and Classification
• Quantum State Reconstruction From Incomplete Data
• Bayesian Field Theory: Nonparametric Approaches to Density Estimation, Regression, Classification, and Inverse Quantum Problems
• How to Implement A Priori Information: A Statistical Mechanics Approach
• Inverse Time-Dependent Quantum Mechanics

Cited by in corpus (4)

• Information field theory for cosmological perturbation reconstruction and non-linear signal analysis
• Reconstruction of signals with unknown spectra in information field theory with parameter uncertainty
• Bayesian analysis of spatially distorted cosmic signals from Poissonian data
• The Bayesian Inversion Problem for Thermal Average Sampling of Quantum Systems