# Analytic Continuation of Quantum Monte Carlo Data by Stochastic Analytical Inference

## TL;DR

This paper introduces a Bayesian-based algorithm for analytic continuation of quantum Monte Carlo data, providing a principled way to estimate energy spectra without ad-hoc regularization choices.

## Contribution

It develops a novel Bayesian inference method for analytic continuation that explicitly calculates weighted averages over spectra, avoiding arbitrary regularization parameters.

## Key findings

- Algorithm successfully applied to quantum Monte Carlo data
- Results compare favorably with maximum entropy methods
- Provides a distribution of spectra as a function of regularization

## Abstract

We present an algorithm for the analytic continuation of imaginary-time quantum Monte Carlo data which is strictly based on principles of Bayesian statistical inference. Within this framework we are able to obtain an explicit expression for the calculation of a weighted average over possible energy spectra, which can be evaluated by standard Monte Carlo simulations, yielding as by-product also the distribution function as function of the regularization parameter. Our algorithm thus avoids the usual ad-hoc assumptions introduced in similar algortihms to fix the regularization parameter. We apply the algorithm to imaginary-time quantum Monte Carlo data and compare the resulting energy spectra with those from a standard maximum entropy calculation.