# Moving Target Monte Carlo

arXiv: https://arxiv.org/abs/2003.04873 · HTML: https://mlsanity.com/paper/2003.04873/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 10 Mar 2020.

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

- [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)

## Abstract (arXiv)

The Markov Chain Monte Carlo (MCMC) methods are popular when considering sampling from a high-dimensional random variable x with possibly unnormalised probability density p and observed data d. However, MCMC requires evaluating the posterior distribution p(x|d) of the proposed candidate x at each iteration when constructing the acceptance rate. This is costly when such evaluations are intractable. In this paper, we introduce a new non-Markovian sampling algorithm called Moving Target Monte Carlo (MTMC). The acceptance rate at n-th iteration is constructed using an iteratively updated approximation of the posterior distribution an(x) instead of p(x|d). The true value of the posterior p(x|d) is only calculated if the candidate x is accepted. The approximation an utilises these evaluations and converges to p as n rightarrow ∞. A proof of convergence and estimation of convergence rate in different situations are given.