IID Sampling from Intractable Distributions

Article Type

Research Article

Publication Title

Sankhya A

Abstract

In this article, we propose a novel methodology for drawing iid realizations from any target distribution on the d-dimensional Euclidean space, for any d≥1. No assumption of compact support is required for the validity of our theory or method. The key idea is to construct an infinite sequence of concentric closed ellipsoids, motivated by the insight that the central ellipsoid tends to capture the modal region, while the regions between successive ellipsoids (ellipsoidal annuli) increasingly represent the tail regions of the distribution. Representing the target distribution as an infinite mixture of component distributions defined on the central ellipsoid and the annuli, we propose a simulation strategy in which a component is first selected with its mixing probability, and then sampled exactly using perfect simulation. The perfect sampling scheme is built upon a minorization inequality for the general Metropolis–Hastings algorithm driven by uniform proposal distributions on the compact ellipsoid and annuli. Unlike most existing work on perfect sampling, our method is not only theoretically valid but also practically applicable to any target distribution on Rd, and is readily parallelizable. We validate the practicality of our approach by generating 10,000 iid realizations from standard distributions such as the normal, Student’s t with 5 degrees of freedom, and Cauchy, for dimensions d=1,5,10,50,100, as well as from a 50-dimensional normal mixture distribution. In all cases, implementation times are reasonable, often less than a minute in our parallel setup, and the results are highly accurate. We further demonstrate the method by generating 10,000 iid realizations from posterior distributions associated with the well-known Challenger data, a Salmonella dataset, and a 160-dimensional spatial example of radionuclide count data on Rongelap Island. In each case, the results are encouraging and computation times remain very reasonable.

DOI

10.1007/s13171-025-00427-4

Publication Date

1-1-2025

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