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:

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

$$\hat{\tau }=-1+2\sum _{t^{\prime }=0}^K{\hat{P}}_{t^{\prime }}$$

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://arviz-devs.github.io/arviz/api/generated/arviz.ess.html

• 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