二元表边际似然及生态推断
The Marginal Likelihood of two-way tables and Ecological Inference
AI总结：
本文提出了一种高效算法用于二元表边际似然的计算，明确了生态推断的条件，并通过模拟验证了方法的有效性。
摘要：
本文推导了二元表边际似然的新结果，明确了生态推断可能的条件，并提出了一种高效算法用于最大化精确的多项式似然。第一部分将Placket(1977)对2x2表边际似然的研究推广到一般的RxC表。在此过程中引入了新的概念工具，并推导了具有固定行和列边际的表集合的几何结构以及扩展的超几何分布的新见解。第二部分，当一组共享相同关联结构的二元表的行和列边际分布观测可用时，提出了一种高效的Fisher评分算法，用于在多项式抽样下最大化精确似然，并通过小规模模拟研究比较所提方法与两种已知方法的性能。
英文摘要：
The paper derives new results on the marginal likelihood of a two-way table which clarify the conditions under which Ecological inference is possible and lead to an efficient algorithm for maximizing the exact multinomial likelihood. The first part generalizes the work of Placket(1977} on the marginal likelihood of a 2 x 2 table to a general R x C table. In doing so, new conceptual tools are introduced and new insights on the geometry of the collection of tables having fixed row and column margins and the extended hypergeometric distribution are derived. In the second part, when observations on the row and the column marginal distributions are available for a collection of two-way tables sharing the same association structure, an efficient Fisher scoring algorithm for maximizing the exact likelihood under multinomial sampling is introduced and a small simulation study is used to compare the performance of the proposed method with two well established ones.
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。
