Living on the Edge: An Unified Approach to Antithetic Sampling

TL;DR

This paper presents a unified framework for antithetic sampling, introducing new schemes with optimality properties, correlation measures, and a CLT, with applications in Monte Carlo methods and Bayesian estimation.

Contribution

It introduces a new class of antithetic schemes that unify existing methods and derives novel properties, including optimality and asymptotic behavior.

Findings

New antithetic schemes with optimal Kullback-Leibler divergence

Closed-form expressions for Kendall's tau and Spearman's rho

A central limit theorem for Monte Carlo estimators

Abstract

We identify recurrent ingredients in the antithetic sampling literature leading to a unified sampling framework. We introduce a new class of antithetic schemes that includes the most used antithetic proposals. This perspective enables the derivation of new properties of the sampling schemes: i) optimality in the Kullback-Leibler sense; ii) closed-form multivariate Kendall's $\tau$ and Spearman's $\rho$; iii)ranking in concordance order and iv) a central limit theorem that characterizes stochastic behavior of Monte Carlo estimators when the sample size tends to infinity. Finally, we provide applications to Monte Carlo integration and Markov Chain Monte Carlo Bayesian estimation.