# Comparison of asymptotic variances of inhomogeneous Markov chains with application to Markov chain Monte Carlo methods

arXiv: https://arxiv.org/abs/1307.3719 · HTML: https://mlsanity.com/paper/1307.3719/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 14 Jul 2013.

## Built on by (most cited first, 1 of 1)

- [Beyond Self-Repellent Kernels: History-Driven Target Towards Efficient Nonlinear MCMC on General Graphs](https://mlsanity.com/paper/2505.18300/) (2025)

## Abstract (arXiv)

In this paper, we study the asymptotic variance of sample path averages for inhomogeneous Markov chains that evolve alternatingly according to two different π-reversible Markov transition kernels P and Q. More specifically, our main result allows us to compare directly the asymptotic variances of two inhomogeneous Markov chains associated with different kernels Pi and Qi, i∈0,1, as soon as the kernels of each pair (P0,P1) and (Q0,Q1) can be ordered in the sense of lag-one autocovariance. As an important application, we use this result for comparing different data-augmentation-type Metropolis-Hastings algorithms. In particular, we compare some pseudo-marginal algorithms and propose a novel exact algorithm, referred to as the random refreshment algorithm, which is more efficient, in terms of asymptotic variance, than the Grouped Independence Metropolis-Hastings algorithm and has a computational complexity that does not exceed that of the Monte Carlo Within Metropolis algorithm.