谁会害怕沃伦纽斯分布？
Who's Afraid of the Wallenius Distribution?
AI总结：
本文探讨沃伦纽斯非中心超几何分布在固定边际列联表分析中的应用，提出似然与贝叶斯推断方法，通过实例验证，简化2×2表分析并解决多组表数值挑战，还构建球面行走Metropolis算法。
摘要：
本文研究沃伦纽斯非中心超几何分布在分析具有两组或多组、两个类别且行边际和样本量（即两个边际）固定的列联表中的应用。该分布的参数被视为权重，这些权重为正且总和为1，因此定义在正则单纯形上。本文提出了基于似然和贝叶斯推断的分析方法，并通过实例进行说明，数据集来自文献，其中一个案例用于生成半合成数据。使用单变量沃伦纽斯分布分析2×2列联表被证明是直接的，其参数为单一权重，可立即转换为所需的优势比。然而，基于多变量沃伦纽斯分布分析两组以上的列联表比两组表的分析更为复杂，具体而言，实现必要计算需要一些数值技巧，特别是通过转换权重将优化问题转化为无约束优化，以及对极小似然值乘以适当因子而不影响推断元素。此外，本文构建了一种新的贝叶斯推断马尔可夫链蒙特卡罗算法，称为球面行走Metropolis算法，该算法在参考单纯形的笛卡尔坐标中实现提议，在正则单纯形的重心坐标中实现Metropolis过滤，两种坐标之间无缝转换。
英文摘要：
This paper is about the use of the Wallenius noncentral hypergeometric distribution for analysing contingency tables with two or more groups and two categories and with row margins and sample size, that is both margins, fixed. The parameters of the distribution are taken to be weights which are positive and sum to one and are thus defined on a regular simplex. The approach to analysis is presented for likelihood-based and Bayesian inference and is illustrated by example, with datasets taken from the literature and, in one case, used to generate semi-synthetic data. The analysis of two-by-two contingency tables using the univariate Wallenius distribution is shown to be straightforward, with the parameter a single weight which translates immediately to the requisite odds and the odds ratio. The analysis of contingency tables with more than two groups based on the multivariate Wallenius distribution was however more nuanced than that of the two-group tables. Specifically, some numerical subtleties were required in order to implement the necessary calculations. In particular, optimisation with respect to the weights was performed by transforming the weights to yield an unconstrained optimisation problem and likelihoods which are extremely small were scaled by an appropriate multiplying factor without compromising the elements of inference. Furthermore, a novel Markov chain Monte Carlo algorithm for Bayesian inference, termed the sphere walk Metropolis, was constructed. The proposal is implemented in Cartesian coordinates on the reference simplex and the Metropolis filter in barycentric coordinates on the regular simplex, with the transition between barycentric and Cartesian coordinates effected seamlessly.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
