# Efficient strategy for the Markov chain Monte Carlo in high-dimension with heavy-tailed target probability distribution

arXiv: https://arxiv.org/abs/1412.6231 · HTML: https://mlsanity.com/paper/1412.6231/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 19 Dec 2014.

## Built on by (most cited first, 5 of 5)

- [Towards a Complete Analysis of Langevin Monte Carlo: Beyond Poincar'e Inequality](https://mlsanity.com/paper/2303.03589/) (2023)
- [Heavy-tailed Sampling via Transformed Unadjusted Langevin Algorithm](https://mlsanity.com/paper/2201.08349/) (2022)
- [Stereographic Markov Chain Monte Carlo](https://mlsanity.com/paper/2205.12112/) (2022)
- [A Separation in Heavy-Tailed Sampling: Gaussian vs. Stable Oracles for Proximal Samplers](https://mlsanity.com/paper/2405.16736/) (2024)
- [Mean-Square Analysis of Discretized Ito Diffusions for Heavy-tailed Sampling](https://mlsanity.com/paper/2303.00570/) (2023)

## Abstract (arXiv)

The purpose of this paper is to introduce a new Markov chain Monte Carlo method and exhibit its efficiency by simulation and high-dimensional asymptotic theory. Key fact is that our algorithm has a reversible proposal transition kernel, which is designed to have a heavy-tailed invariant probability distribution. The high-dimensional asymptotic theory is studied for a class of heavy-tailed target probability distribution. As the number of dimension of the state space goes to infinity, we will show that our algorithm has a much better convergence rate than that of the preconditioned Crank Nicolson (pCN) algorithm and the random-walk Metropolis (RWM) algorithm. We also show that our algorithm is at least as good as the pCN algorithm and better than the RWM algorithm for light-tailed target probability distribution.