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arXiv · 2403.20313

Towards a turnkey approach to unbiased Monte Carlo estimation of smooth functions of expectations

Nicolas Chopin·Francesca R. Crucinio·Sumeetpal S. Singh
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Abstract

Given a smooth function $f$, we develop a general approach to turn Monte Carlo samples with expectation $m$ into an unbiased estimate of $f(m)$. Specifically, we develop estimators that are based on randomly truncating the Taylor series expansion of $f$ and estimating the coefficients of the truncated series. We derive their properties and propose a strategy to set their tuning parameters -- which depend on $m$ -- automatically, with a view to make the whole approach simple to use. We develop our methods for the specific functions $f(x)=\log x$ and $f(x)=1/x$, as they arise in several statistical applications such as maximum likelihood estimation of latent variable models and Bayesian inference for un-normalised models. Detailed numerical studies are performed for a range of applications to determine how competitive and reliable the proposed approach is.

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Nicolas Chopin, Francesca R. Crucinio, Sumeetpal S. Singh. 2024-03-29. Towards a turnkey approach to unbiased Monte Carlo estimation of smooth functions of expectations. https://arxiv.org/abs/2403.20313

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