Estimate a lower bound on effective sample size for each independent chain.

Roughly speaking, "effective sample size" (ESS) is the size of an iid sample with the same variance as state.

mcmc_effective_sample_size(
  states,
  filter_threshold = 0,
  filter_beyond_lag = NULL,
  name = NULL
)

Arguments

states	Tensor or list of Tensor objects. Dimension zero should index identically distributed states.
filter_threshold	Tensor or list of Tensor objects. Must broadcast with state. The auto-correlation sequence is truncated after the first appearance of a term less than filter_threshold. Setting to NULL means we use no threshold filter. Since |R_k| <= 1, setting to any number less than -1 has the same effect.
filter_beyond_lag	Tensor or list of Tensor objects. Must be int-like and scalar valued. The auto-correlation sequence is truncated to this length. Setting to NULL means we do not filter based on number of lags.
name	name to prepend to created ops.

Value

Tensor or list of Tensor objects. The effective sample size of each component of states. Shape will be states$shape[1:].

Details

More precisely, given a stationary sequence of possibly correlated random variables X_1, X_2,...,X_N, each identically distributed ESS is the number such that Variance{ N**-1 * Sum{X_i} } = ESS**-1 * Variance{ X_1 }.

If the sequence is uncorrelated, ESS = N. In general, one should expect ESS <= N, with more highly correlated sequences having smaller ESS.

See also

Other mcmc_functions: mcmc_potential_scale_reduction(), mcmc_sample_annealed_importance_chain(), mcmc_sample_chain(), mcmc_sample_halton_sequence()