Description
Approximating Evidence via Bounded Harmonic Means.
Description
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) <doi:10.48550/arXiv.2510.20617>.
README.md
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 atpost_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 anecmlefit.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