A debiased Bernoulli factory and unbiased estimation of a probability
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| Main Authors: | , , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866912623152332800 |
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| author | Koskela, Jere Karvonen, Toni Łatuszyński, Krzysztof Spanò, Dario |
| author_facet | Koskela, Jere Karvonen, Toni Łatuszyński, Krzysztof Spanò, Dario |
| contents | Given a known function $f : [0, 1] \mapsto (0, 1)$ and a random but almost surely finite number of independent, Ber$(x)$-distributed random variables with unknown $x \in [0, 1]$, we construct an unbiased, $[0, 1]$-valued estimator of the probability $f(x) \in (0, 1)$. Our estimator is based on so-called debiasing, or randomly truncating a telescopic series of consistent estimators. Constructing these consistent estimators from the coefficients of a particular Bernoulli factory for $f$ yields provable upper and lower bounds for our unbiased estimator. Our result can be thought of as a novel Bernoulli factory with the appealing property that the required number of Ber$(x)$-distributed random variates is independent of their outcomes, and also as constructive example of the so-called $f$-factory. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_01941 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A debiased Bernoulli factory and unbiased estimation of a probability Koskela, Jere Karvonen, Toni Łatuszyński, Krzysztof Spanò, Dario Probability Statistics Theory Computation 60-08, 62-08, 65C20 Given a known function $f : [0, 1] \mapsto (0, 1)$ and a random but almost surely finite number of independent, Ber$(x)$-distributed random variables with unknown $x \in [0, 1]$, we construct an unbiased, $[0, 1]$-valued estimator of the probability $f(x) \in (0, 1)$. Our estimator is based on so-called debiasing, or randomly truncating a telescopic series of consistent estimators. Constructing these consistent estimators from the coefficients of a particular Bernoulli factory for $f$ yields provable upper and lower bounds for our unbiased estimator. Our result can be thought of as a novel Bernoulli factory with the appealing property that the required number of Ber$(x)$-distributed random variates is independent of their outcomes, and also as constructive example of the so-called $f$-factory. |
| title | A debiased Bernoulli factory and unbiased estimation of a probability |
| topic | Probability Statistics Theory Computation 60-08, 62-08, 65C20 |
| url | https://arxiv.org/abs/2510.01941 |