Approximating Evidence via Bounded Harmonic Means

Implements the Elliptical Covering Marginal Likelihood Estimator (ECMLE), a geometric method for approximating marginal likelihood from posterior draws and log-posterior evaluations. The method constructs a collection of non-overlapping ellipsoids in a high-posterior-density region, computes the covered volume, and combines this with posterior sample coverage to estimate model evidence. It is designed to stabilize harmonic-mean-based evidence approximation and can be applied in multimodal settings. The methodology is described in Naderi et al. (2025) .

ECMLE

ECMLE is an R package for the Elliptical Covering Marginal Likelihood Estimator. It implements a geometric marginal-likelihood estimator based on posterior draws, log-posterior evaluations, and ellipsoidal coverings of a high-posterior-density region.

The method is described in:

Naderi et al. (2025). Approximating Evidence via Bounded Harmonic Means. https://doi.org/10.48550/arXiv.2510.20617

Installation

install.packages("ECMLE")

Main function

ecmle(post_samples, lps, log_post_fn, hpd_level = 0.75)

Arguments

• post_samples: matrix of posterior draws, one row per draw.
• lps: numeric vector of log-posterior values at post_samples.
• log_post_fn: function returning the log unnormalized posterior density (log prior + log likelihood) at a parameter vector.
• hpd_level: HPD fraction used to define the packing region.

Minimal example

set.seed(1)
post_samples <- cbind(rnorm(400), rnorm(400))
lps <- apply(post_samples, 1, function(z) sum(dnorm(z, log = TRUE)))
log_post_fn <- function(theta) sum(dnorm(theta, log = TRUE))

fit <- ecmle(
  post_samples = post_samples,
  lps          = lps,
  log_post_fn  = log_post_fn,
  hpd_level    = 0.75
)
print(fit)
plot(fit)

Package contents

• ecmle(): estimates the log marginal likelihood.
• summary(): returns a compact summary of an ecmle fit.
• plot(): shows the running estimate across the evaluation half-sample.
• plot_ecmle_2d(), draw_ellipse_2d(): 2-D visualisation of fitted ellipsoids.
• pair_plot(): lower-triangular pair plot for posterior sample matrices.
• rosenbrock_generate_data(), rosenbrock_exact_posterior(), rosenbrock_log_post(), rosenbrock_log_post_vec(): Rosenbrock (banana) posterior benchmark functions.

License

GPL-3