Relative Entropy Between Two Sample Ensembles (Gaussian approximation)

Convenience wrapper around relative_entropy() for ensemble inputs (for example a PESTO posterior ensemble): each ensemble is summarised by its sample mean and covariance and the Gaussian relative entropy is returned. This is a moment-matched approximation – exact when the ensembles are Gaussian and a second-order surrogate otherwise.

Usage

relative_entropy_ensemble(p_draws, q_draws)

Arguments

p_draws

Numeric matrix n_p x k (or vector for k = 1): draws from p (the smoother ensemble, for ACI).

q_draws

Numeric matrix n_q x k (or vector): draws from q (the filter ensemble). Must have the same number of columns as p_draws.

Value

A single non-negative numeric: the moment-matched relative entropy.

See also

relative_entropy()

Examples

set.seed(1)
p <- matrix(rnorm(2000), ncol = 2)
q <- matrix(rnorm(2000), ncol = 2) + 1
relative_entropy_ensemble(p, q)
#> [1] 0.9801008