Bayesian field theory and approximate symmetries
J. C. Lemm · AIP conference proceedings · 2001
Nonparametric Bayesian approaches to density estimation (“Bayesian field theories”) have typically to be solved numerically on a lattice. This is often numerically quite expensive. The Paper wants to show that such numerical calculations are nowadays feasible for some interesting problem classes. In particular, Bayesian field theories are defined by 1. a likelihood model, being a probabilistic description of the measurement process of observational data. and 2. a prior model, determining the generalization behavior of the theory by implementing available a priori knowledge. In this Paper some variations of prior and likelihood models are discussed: First, the implementation of approximate symmetries with Gaussian process priors is demonstrated for approximate periodic and for approximate fractal functions. Second, besides a discussion of the classical likelihood models of general density estimation and regression, special emphasis is put on the likelihood model of quantum theory to treat the inverse problem of reconstructing potentials of quantum systems from a finite number of observational data.