Autocorrelation Analysis¶
A good heuristic for assessing convergence of samplings is the integrated
autocorrelation time. emcee
includes tools for computing this and the
autocorrelation function itself. More details can be found in
Autocorrelation analysis & convergence.

emcee.autocorr.
integrated_time
(x, c=5, tol=50, quiet=False)¶ Estimate the integrated autocorrelation time of a time series.
This estimate uses the iterative procedure described on page 16 of Sokal’s notes to determine a reasonable window size.
 Parameters
x – The time series. If multidimensional, set the time axis using the
axis
keyword argument and the function will be computed for every other axis.c (Optional[float]) – The step size for the window search. (default:
5
)tol (Optional[float]) – The minimum number of autocorrelation times needed to trust the estimate. (default:
50
)quiet (Optional[bool]) – This argument controls the behavior when the chain is too short. If
True
, give a warning instead of raising anAutocorrError
. (default:False
)
 Returns
 An estimate of the integrated autocorrelation time of
the time series
x
computed along the axisaxis
.
 Return type
float or array
 Raises
 AutocorrError: If the autocorrelation time can’t be reliably estimated
from the chain and
quiet
isFalse
. This normally means that the chain is too short.

emcee.autocorr.
function_1d
(x)¶ Estimate the normalized autocorrelation function of a 1D series
 Parameters
x – The series as a 1D numpy array.
 Returns
The autocorrelation function of the time series.
 Return type
array