Revisiting Estimation of Number of Trials in Binomial Distribution
综述了二项分布中试验次数n的估计方法，提出一种基于边际似然的新估计器，在多种场景下性能有竞争力甚至更优。
Summary Estimating the parameter when is known or simultaneous estimation of and of the binomial distribution based on independent observations has been considered by many authors over the last several decades. A range of estimators have been proposed, and questions regarding asymptotic and small sample properties received adequate treatment. In this paper, we provide an extensive review and a comprehensive performance comparison of the estimators from the literature. We propose a conceptually simple estimator of that uses the marginal likelihood when is integrated out by simultaneous optimisation w.r.t. and the hyperparameters. We compare the proposed estimator with various existing estimators and find its performance competitive and, in some scenarios, superior.