{"ID":2861448,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2510.01941","arxiv_id":"2510.01941","title":"A debiased Bernoulli factory and unbiased estimation of a probability","abstract":"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.","short_abstract":"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 r...","url_abs":"https://arxiv.org/abs/2510.01941","url_pdf":"https://arxiv.org/pdf/2510.01941v1","authors":"[\"Jere Koskela\",\"Toni Karvonen\",\"Krzysztof Łatuszyński\",\"Dario Spanò\"]","published":"2025-10-02T12:04:19Z","proceeding":"math.PR","tasks":"[\"math.PR\",\"math.ST\",\"stat.CO\"]","methods":"[]","has_code":false}