boltzkit.evaluation.density_based.ess

Functions

`get_forward_ess`(log_weights)	Compute the forward effective sample size (ESS) from log-importance weights.
`get_reverse_ess`(log_weights)	Compute the reverse effective sample size (ESS) from log-importance weights.

boltzkit.evaluation.density_based.ess.get_reverse_ess(log_weights: ndarray) → float[source]

Compute the reverse effective sample size (ESS) from log-importance weights.

Reverse ESS measures how well a proposal distribution \(q(x)\) covers a target distribution \(p(x)\) in importance sampling.

Using weights \(w_i = \exp(\log p(x_i) - \log q(x_i))\), the ESS is:

\[\mathrm{ESS} = \frac{\left(\sum_i w_i\right)^2}{N \sum_i w_i^2}\]

Log-form computation is used for numerical stability.

Parameters:

log_weights (np.ndarray) –

Log importance weights:

\[\log w_i = \log p(x_i) - \log q(x_i)\]

where \(x_i \sim q(x)\).

Returns:

Reverse ESS in \((0, 1]\), representing the effective fraction of useful samples.

Return type:

float

boltzkit.evaluation.density_based.ess.get_forward_ess(log_weights: ndarray) → float[source]

Compute the forward effective sample size (ESS) from log-importance weights.

Forward ESS measures overlap quality when samples are drawn from the target distribution \(p(x)\) and reweighted toward a proposal \(q(x)\).

It is defined as:

\[\mathrm{ESS} = \frac{1}{\mathbb{E}_p[w] \; \mathbb{E}_p[1/w]}\]

where \(w = \exp(\log p(x) - \log q(x))\).