latqcdtools.statistics.autocorrelation
=============

`getTauInt(ts, nbins, tpickMax, acoutfileName='acor.d', showPlot=False)`
 
    Given a time series, return estimates for the integrated autocorrelation time and its error.

    INPUT:
         tpickMax--The largest nt where you think your estimate might become unreliable.
            nbins--The number of jackknife bins (for estimating the error in tau_int)
               ts--Time series array of measurements. Must be taken from equilibrium ensemble so that
                   time translation invariance holds. List must be in order of markov chain generation

    OUTPUT:
          tau_int--Estimate for integrated autocorrelation time.
         tau_inte--Its (jackknife) error bar.
           itpick--The Monte Carlo separation at which this method found its estimate for tau_int. 
    
`remove1Jackknife(ts) -> numpy.ndarray`
 
    Create remove-1 jackknife list from 1-d series.

    Args:
        ts (array-like): time series 

    Returns:
        np.array: 1-d array of jackknife means 
    
`tauint(nt, ts, xhat=None) -> numpy.ndarray`
 
    Given a time series, calculate estimators for its integrated autocorrelation time  at each Markov time separation.

    INPUT:
         nt--The largest you think tau_int could be.
         ts--Time series array of measurments. Must be taken from equilibrium ensemble so that
             time translation invariance holds. List must be in order of Markov chain generation.
       xhat--True mean of time series (if you know it).

    OUTPUT:
      acint--List of integrated autocorrelation times. 
      
`tauintj(nt, nbins, ts, xhat=None) -> numpy.ndarray`
 
    Given a time series, calculate jackknife bins of integrated autocorrelation time for each Markov time separation.

    INPUT:
          nt--The largest nt at which you think your estimate for tau_int could lie.
       nbins--The number of jackknife bins.
          ts--Time series array of measurements. Must be taken from equilibrium ensemble so that
              time translation invariance holds. List must be in order of markov chain generation
        xhat--True mean of time series (if you know it).

    OUTPUT:
      acintj--2D list indexed by time, then bin number acintj[it][ibin]