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Generate new points from multiple spanning ellipsoids

Source: R/multi_ellipsoid.R
multi_ellipsoid.Rd

Partitions the prior space into a set of ellipsoids whose union bounds the live set. New points are created by randomly selecting an ellipsoid (weighted by their respective volumes), then using it to generate a random point as in unif_ellipsoid. Effective for multimodal posteriors where a single ellipsoid would be inefficient.

Usage

multi_ellipsoid(enlarge = 1.25)

Arguments

enlarge

[double(1)]
Factor by which to inflate the bounding ellipsoid's volume before sampling (see Details). Must be at least 1.0.

Value

[multi_ellipsoid], a named list that inherits from [ernest_lrps].

Details

Nested likelihood contours for multimodal distributions are poorly represented by a single ellipsoid. This method fits multiple ellipsoids to better capture disconnected or elongated regions.

Ellipsoids are generated using the following procedure:

  1. A single ellipsoid is fit to the live set, with volume \(V\).

  2. The live set is clustered into two groups using k-means clustering.

  3. Ellipsoids are fit to each cluster.

  4. The split ellipsoids are accepted if both ellipsoids are non-degenerate, and if the combined volume of the split ellipsoids is significantly smaller than the original ellipsoid (calculated using Bayes' Information Criterion).

  5. Steps 2–4 are repeated recursively on each new ellipsoid until no further splits are accepted, updating \(V\) to the volume of the currently split ellipsoid.

References

  • Feroz, F., Hobson, M. P., Bridges, M. (2009) MULTINEST: An Efficient and Robust Bayesian Inference Tool for Cosmology and Particle Physics. Monthly Notices of the Royal Astronomical Society. 398(4), 1601–1614. doi:10.1111/j.1365-2966.2009.14548.x

  • Speagle, J. S. (2020). Dynesty: A Dynamic Nested Sampling Package for Estimating Bayesian Posteriors and Evidences. Monthly Notices of the Royal Astronomical Society, 493, 3132–3158. doi:10.1093/mnras/staa278

See also

Other ernest_lrps: rwmh_cube(), slice_rectangle(), unif_cube(), unif_ellipsoid()

Examples

data(example_run)
lrps <- multi_ellipsoid(enlarge = 1.25)

ernest_sampler(example_run$log_lik_fn, example_run$prior, sampler = lrps)
#> Nested sampling run specification:
#> * No. points: 500
#> * Sampling method: Uniform sampling within bounding ellipsoids (enlarged by
#> 1.25)
#> * Prior: uniform prior distribution with 3 dimensions (x, y, and z)