# A Review of Multiple Try MCMC algorithms for Signal Processing

arXiv: https://arxiv.org/abs/1801.09065 · HTML: https://mlsanity.com/paper/1801.09065/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 27 Jan 2018.

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

- [A Survey of Monte Carlo Methods for Parameter Estimation](https://mlsanity.com/paper/2107.11820/) (2021)
- [Compressed particle methods for expensive models with application in Astronomy and Remote Sensing](https://mlsanity.com/paper/2107.08465/) (2021)
- [Covid19 Reproduction Number: Credibility Intervals by Blockwise Proximal Monte Carlo Samplers](https://mlsanity.com/paper/2203.09142/) (2022)
- [Adaptive posterior distributions for uncertainty analysis of covariance matrices in Bayesian inversion problems for multioutput signals](https://mlsanity.com/paper/2501.01148/) (2025)
- [Eryn : A multi-purpose sampler for Bayesian inference](https://mlsanity.com/paper/2303.02164/) (2023)

## Abstract (arXiv)

Many applications in signal processing require the estimation of some parameters of interest given a set of observed data. More specifically, Bayesian inference needs the computation of it a-posteriori estimators which are often expressed as complicated multi-dimensional integrals. Unfortunately, analytical expressions for these estimators cannot be found in most real-world applications, and Monte Carlo methods are the only feasible approach. A very powerful class of Monte Carlo techniques is formed by the Markov Chain Monte Carlo (MCMC) algorithms. They generate a Markov chain such that its stationary distribution coincides with the target posterior density. In this work, we perform a thorough review of MCMC methods using multiple candidates in order to select the next state of the chain, at each iteration. With respect to the classical Metropolis-Hastings method, the use of multiple try techniques foster the exploration of the sample space. We present different Multiple Try Metropolis schemes, Ensemble MCMC methods, Particle Metropolis-Hastings algorithms and the Delayed Rejection Metropolis technique. We highlight limitations, benefits, connections and differences among the different methods, and compare them by numerical simulations.