# MCMC-driven importance samplers

arXiv: https://arxiv.org/abs/2105.02579 · HTML: https://mlsanity.com/paper/2105.02579/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 8 of its 65 references that are in the map.
- First posted on arXiv 6 May 2021.

## Builds on (most cited first, 8 of 8)

- [Marginal likelihood computation for model selection and hypothesis testing: an extensive review](https://mlsanity.com/paper/2005.08334/) (2020)
- [Asymptotically Exact, Embarrassingly Parallel MCMC](https://mlsanity.com/paper/1311.4780/) (2013)
- [Layered Adaptive Importance Sampling](https://mlsanity.com/paper/1505.04732/) (2015)
- [Convergence rates for optimised adaptive importance samplers](https://mlsanity.com/paper/1903.12044/) (2019)
- [A Joint introduction to Gaussian Processes and Relevance Vector Machines with Connections to Kalman filtering and other Kernel Smoothers](https://mlsanity.com/paper/2009.09217/) (2020)
- [Deep Importance Sampling based on Regression for Model Inversion and Emulation](https://mlsanity.com/paper/2010.10346/) (2020)
- [Markov Chain Importance Sampling -- a highly efficient estimator for MCMC](https://mlsanity.com/paper/1805.07179/) (2018)
- [Likelihood Inflating Sampling Algorithm](https://mlsanity.com/paper/1605.02113/) (2016)

## Built on by (most cited first, 3 of 3)

- [Global convergence of optimized adaptive importance samplers](https://mlsanity.com/paper/2201.00409/) (2022)
- [Adaptive posterior distributions for uncertainty analysis of covariance matrices in Bayesian inversion problems for multioutput signals](https://mlsanity.com/paper/2501.01148/) (2025)
- [From Minimax Optimal Importance Sampling to Uniformly Ergodic Importance-tempered MCMC](https://mlsanity.com/paper/2506.19186/) (2025)

## Abstract (arXiv)

Monte Carlo sampling methods are the standard procedure for approximating complicated integrals of multidimensional posterior distributions in Bayesian inference. In this work, we focus on the class of Layered Adaptive Importance Sampling (LAIS) scheme, which is a family of adaptive importance samplers where Markov chain Monte Carlo algorithms are employed to drive an underlying multiple importance sampling scheme. The modular nature of LAIS allows for different possible implementations, yielding a variety of different performance and computational costs. In this work, we propose different enhancements of the classical LAIS setting in order to increase the efficiency and reduce the computational cost, of both upper and lower layers. The different variants address computational challenges arising in real-world applications, for instance with highly concentrated posterior distributions. Furthermore, we introduce different strategies for designing cheaper schemes, for instance, recycling samples generated in the upper layer and using them in the final estimators in the lower layer. Different numerical experiments, considering several challenging scenarios, show the benefits of the proposed schemes comparing with benchmark methods presented in the literature.