IID Sampling from Intractable Multimodal and Variable-Dimensional Distributions

TL;DR

This paper extends a novel iid sampling method to handle complex multimodal and variable-dimensional distributions, demonstrating its effectiveness on high-dimensional normal mixtures and real-world data.

Contribution

It introduces extensions of Bhattacharya's iid sampling method to multimodal and variable-dimensional distributions, broadening its applicability.

Findings

Successfully sampled from high-dimensional normal mixtures

Extended iid sampling to variable-dimensional data

Demonstrated applicability on real-world acidity data

Abstract

Bhattacharya (2021b) has introduced a novel methodology for generating iid realizations from any target distribution on the Euclidean space, irrespective of dimensionality. In this article, our purpose is two-fold. We first extend the method for obtaining iid realizations from general multimodal distributions, and illustrate with a mixture of two 50-dimensional normal distributions. Then we extend the iid sampling method for fixed-dimensional distributions to variable-dimensional situations and illustrate with a variable-dimensional normal mixture modeling of the well-known "acidity data", with further demonstration of the applicability of the iid sampling method developed for multimodal distributions.