How does one determine if a Monte Carlo simulation has converged?

It turns out the determination of equilibration length of a noisy simulation is not as easy as one may initially expect.

J. Chem. Theory Comput. 2016, 12, 1799−1805 (DOI: 10.1021/acs.jctc.5b00784)

J. Chem. Phys. 2004 (DOI: 10.1063/1.1638996)