# Optimality in Noisy Importance Sampling

arXiv: https://arxiv.org/abs/2201.02432 · HTML: https://mlsanity.com/paper/2201.02432/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 13 of its 34 references that are in the map.
- First posted on arXiv 7 Jan 2022.

## Builds on (most cited first, 13 of 13)

- [Bayesian Optimization for Likelihood-Free Inference of Simulator-Based Statistical Models](https://mlsanity.com/paper/1501.03291/) (2015)
- [On Markov chain Monte Carlo methods for tall data](https://mlsanity.com/paper/1505.02827/) (2015)
- [A survey on policy search algorithms for learning robot controllers in a handful of trials](https://mlsanity.com/paper/1807.02303/) (2018)
- [Marginal likelihood computation for model selection and hypothesis testing: an extensive review](https://mlsanity.com/paper/2005.08334/) (2020)
- [Variational Bayesian Monte Carlo with Noisy Likelihoods](https://mlsanity.com/paper/2006.08655/) (2020)
- [A Survey of Monte Carlo Methods for Parameter Estimation](https://mlsanity.com/paper/2107.11820/) (2021)
- [Speeding Up MCMC by Efficient Data Subsampling](https://mlsanity.com/paper/1404.4178/) (2014)
- [Parallel Gaussian process surrogate Bayesian inference with noisy likelihood evaluations](https://mlsanity.com/paper/1905.01252/) (2019)
- [Active emulation of computer codes with Gaussian processes -- Application to remote sensing](https://mlsanity.com/paper/1912.06552/) (2019)
- [Ensemble Inference Methods for Models With Noisy and Expensive Likelihoods](https://mlsanity.com/paper/2104.03384/) (2021)
- [A survey of Monte Carlo methods for noisy and costly densities with application to reinforcement learning and ABC](https://mlsanity.com/paper/2108.00490/) (2021)
- [Adaptive quadrature schemes for Bayesian inference via active learning](https://mlsanity.com/paper/2006.00535/) (2020)
- [Importance sampling squared for Bayesian inference in latent variable models](https://mlsanity.com/paper/1309.3339/) (2013)

## Built on by (most cited first, 2 of 2)

- [Adaptive posterior distributions for uncertainty analysis of covariance matrices in Bayesian inversion problems for multioutput signals](https://mlsanity.com/paper/2501.01148/) (2025)
- [CAMEO: Curiosity Augmented Metropolis for Exploratory Optimal Policies](https://mlsanity.com/paper/2205.09433/) (2022)

## Abstract (arXiv)

In this work, we analyze the noisy importance sampling (IS), i.e., IS working with noisy evaluations of the target density. We present the general framework and derive optimal proposal densities for noisy IS estimators. The optimal proposals incorporate the information of the variance of the noisy realizations, proposing points in regions where the noise power is higher. We also compare the use of the optimal proposals with previous optimality approaches considered in a noisy IS framework.