Fitting a sum of exponentials to lattice correlation functions using a non-uniform prior

Abstract

Excited states are extracted from lattice correlation functions using a non-uniform prior on the model parameters. Models for both a single exponential and a sum of exponentials are considered, as well as an alternate model for the orthogonalization of the correlation functions. Results from an analysis of torelon and glueball operators indicate the Bayesian methodology compares well with the usual interpretation of effective mass tables produced by a variational procedure. Applications of the methodology are discussed.

Prediction of particle type from measurements of particle location: A physicist's approach to Bayesian classification

“…The essential difference between inductive and deductive methods is that the former inverts the model to predict the data whereas the latter inverts the data to predict the model-see Ref. [9] for an explicit example regarding sums of exponential functions and Ref. [10] as regards the Fourier transform.…”

Composite parameterization and Haar measure for all unitary and special unitary groups

“…For all these objects we found representations containing the minimal number of parameters needed. Due to its concise notation, simple implementation and computational benefits it has already found widespread applications in research on lattice correlation functions [5], quantum nonlocality [6], genuine multipartite entanglement [7,8,9] and quantum secret sharing [10].…”