Towards a turnkey approach to unbiased Monte Carlo estimation of smooth functions of expectations
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| Main Authors: | , , |
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| Format: | Preprint |
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2024
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| _version_ | 1866916667026571264 |
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| author | Chopin, Nicolas Crucinio, Francesca R. Singh, Sumeetpal S. |
| author_facet | Chopin, Nicolas Crucinio, Francesca R. Singh, Sumeetpal S. |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_20313 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Towards a turnkey approach to unbiased Monte Carlo estimation of smooth functions of expectations Chopin, Nicolas Crucinio, Francesca R. Singh, Sumeetpal S. Methodology Computation 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. |
| title | Towards a turnkey approach to unbiased Monte Carlo estimation of smooth functions of expectations |
| topic | Methodology Computation |
| url | https://arxiv.org/abs/2403.20313 |