arviz.ess#

arviz.ess(data, *, var_names=None, method='bulk', relative=False, prob=None, dask_kwargs=None)[source]#

Calculate estimate of the effective sample size (ess).

Parameters:

dataobj

Any object that can be converted to an arviz.InferenceData object. Refer to documentation of arviz.convert_to_dataset() for details. For ndarray: shape = (chain, draw). For n-dimensional ndarray transform first to dataset with arviz.convert_to_dataset().

var_namesstr or list of str

Names of variables to include in the return value Dataset.

methodstr, optional, default “bulk”

Select ess method. Valid methods are:

“bulk”
“tail” # prob, optional
“quantile” # prob
“mean” (old ess)
“sd”
“median”
“mad” (mean absolute deviance)
“z_scale”
“folded”
“identity”
“local”

relativebool

Return relative ess ress = ess / n

probfloat, or tuple of two floats, optional

probability value for “tail”, “quantile” or “local” ess functions.

dask_kwargsdict, optional

Dask related kwargs passed to wrap_xarray_ufunc().

Returns:

xarray.Dataset: Return the effective sample size, \(\hat{N}_{eff}\)

See also

arviz.rhat: Compute estimate of rank normalized splitR-hat for a set of traces.
arviz.mcse: Calculate Markov Chain Standard Error statistic.
plot_ess: Plot quantile, local or evolution of effective sample sizes (ESS).
arviz.summary: Create a data frame with summary statistics.

Notes

The basic ess (\(N_{\mathit{eff}}\)) diagnostic is computed by:

\[\hat{N}_{\mathit{eff}} = \frac{MN}{\hat{\tau}}\]

\[\hat{\tau} = -1 + 2 \sum_{t'=0}^K \hat{P}_{t'}\]

where \(M\) is the number of chains, \(N\) the number of draws, \(\hat{\rho}_t\) is the estimated _autocorrelation at lag \(t\), and \(K\) is the last integer for which \(\hat{P}_{K} = \hat{\rho}_{2K} + \hat{\rho}_{2K+1}\) is still positive.

The current implementation is similar to Stan, which uses Geyer’s initial monotone sequence criterion (Geyer, 1992; Geyer, 2011).

References

Vehtari et al. (2019) see https://arxiv.org/abs/1903.08008
https://mc-stan.org/docs/2_18/reference-manual/effective-sample-size-section.html Section 15.4.2
Gelman et al. BDA (2014) Formula 11.8

Examples

Calculate the effective_sample_size using the default arguments:

In [1]: import arviz as az
   ...: data = az.load_arviz_data('non_centered_eight')
   ...: az.ess(data)
   ...: 
Out[1]: 
<xarray.Dataset>
Dimensions:  (school: 8)
Coordinates:
  * school   (school) object 'Choate' 'Deerfield' ... "St. Paul's" 'Mt. Hermon'
Data variables:
    mu       float64 1.65e+03
    theta_t  (school) float64 2.058e+03 2.51e+03 ... 2.455e+03 2.757e+03
    tau      float64 1.115e+03
    theta    (school) float64 1.942e+03 2.199e+03 ... 2.079e+03 2.106e+03

Calculate the ress of some of the variables

In [2]: az.ess(data, relative=True, var_names=["mu", "theta_t"])
Out[2]: 
<xarray.Dataset>
Dimensions:  (school: 8)
Coordinates:
  * school   (school) object 'Choate' 'Deerfield' ... "St. Paul's" 'Mt. Hermon'
Data variables:
    mu       float64 0.8252
    theta_t  (school) float64 1.029 1.255 1.14 1.106 0.9535 1.198 1.228 1.378

Calculate the ess using the “tail” method, leaving the prob argument at its default value.

In [3]: az.ess(data, method="tail")
Out[3]: 
<xarray.Dataset>
Dimensions:  (school: 8)
Coordinates:
  * school   (school) object 'Choate' 'Deerfield' ... "St. Paul's" 'Mt. Hermon'
Data variables:
    mu       float64 1.088e+03
    theta_t  (school) float64 1.501e+03 1.4e+03 1.301e+03 ... 1.51e+03 1.56e+03
    tau      float64 827.9
    theta    (school) float64 1.745e+03 1.53e+03 ... 1.403e+03 1.521e+03