  The performance of Markov chain Monte Carlo calculations is determined by
both ensemble variance of the Monte Carlo estimator and autocorrelation of the
Markov process. In order to study autocorrelation, binning analysis is commonly
used, where the autocorrelation is estimated from results grouped into bins of
logarithmically increasing sizes.
  In this paper, we show that binning analysis comes with a bias that can be
eliminated by combining bin sizes. We then show binning analysis can be
performed on-the-fly with linear overhead in time and logarithmic overhead in
memory with respect to the sample size. We then show that binning analysis
contains information not only about the integrated effect of autocorrelation,
but can be used to estimate the spectrum of autocorrelation lengths, yielding
the height of phase space barriers in the system. Finally, we revisit the Ising
model and apply the proposed method to recover its autocorrelation spectra.
