hopsy.ess#

class hopsy.ess(data, series=0, method='bulk', relative=False, prob=None, dask_kwargs=None)#

Calculate estimate of the effective sample size (ess).

Parameters:

  • data (numpy.ndarray) – MCMC samples with data.shape == (n_chains, n_draws, dim).

  • series (int) – Compute a series of effective sample sizes every series samples, so ess will be computed for data[:,:n] for n in range(series, n_draws+1, series). For the default value series==0, ess will be computed only once for the whole data.

  • method (str) –

    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”

  • relative (bool) – Return relative ess ress = ess / n

  • prob (float, or tuple of two floats, optional) – probability value for “tail”, “quantile” or “local” ess functions.

  • n_procs (int = 1) – In combination with “series”: compute series of ess in parallel using n_procs subprocesses.

  • dask_kwargs (dict, optional) – Dask related kwargs passed to wrap_xarray_ufunc().

Returns:

Return the effective sample size, \(\hat{N}_{eff}\)

Return type:

numpy.ndarray

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

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