Bounding statistical errors in lattice field theory simulations

Simulations of strongly interacting lattice field theories are typically performed using Markov chain Monte Carlo algorithms. Therefore estimators of statistical errors must incorporate the effect of autocorrelations by integrating the corresponding autocorrelation function. Since in practical calculations its integral is truncated to a finite window, in this work we propose a stopping criterion based on upper and lower bounds of the autocorrelation function. We examine its application to both traditional Monte Carlo analysis and the recently introduced master-field approach. By leveraging both bounds, we introduce an automatic windowing procedure which we test on numerical simulations of a few simplified toy models.