# On Unbiased Estimation for Discretized Models

arXiv: https://arxiv.org/abs/2102.12230 · HTML: https://mlsanity.com/paper/2102.12230/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 24 Feb 2021.

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

- [Bayesian Deep Learning with Multilevel Trace-class Neural Networks](https://mlsanity.com/paper/2203.12961/) (2022)
- [Unbiased Estimation using Underdamped Langevin Dynamics](https://mlsanity.com/paper/2206.07202/) (2022)
- [Unbiased Estimation of the Gradient of the Log-Likelihood for a Class of Continuous-Time State-Space Models](https://mlsanity.com/paper/2105.11522/) (2021)

## Abstract (arXiv)

In this article, we consider computing expectations w.r.t. probability measures which are subject to discretization error. Examples include partially observed diffusion processes or inverse problems, where one may have to discretize time and/or space, in order to practically work with the probability of interest. Given access only to these discretizations, we consider the construction of unbiased Monte Carlo estimators of expectations w.r.t. such target probability distributions. It is shown how to obtain such estimators using a novel adaptation of randomization schemes and Markov simulation methods. Under appropriate assumptions, these estimators possess finite variance and finite expected cost. There are two important consequences of this approach: (i) unbiased inference is achieved at the canonical complexity rate, and (ii) the resulting estimators can be generated independently, thereby allowing strong scaling to arbitrarily many parallel processors. Several algorithms are presented, and applied to some examples of Bayesian inference problems, with both simulated and real observed data.