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.

翻译：本文推导了关于双向列联表边际似然的新结果，这些结果阐明了生态推断可行的条件，并导出了最大化精确多项似然的高效算法。第一部分将Placket(1977)关于2×2表边际似然的研究推广至一般的R×C表。在此过程中，引入了新的概念工具，并对具有固定行边际与列边际的列联表集合的几何结构以及扩展超几何分布获得了新的认识。第二部分针对一组具有相同关联结构的双向列联表，在可获得其行边际与列边际分布观测数据的情况下，提出了一种用于最大化多项抽样下精确似然的Fisher评分算法，并通过小型模拟研究比较了所提方法与两种经典方法的性能。