关于社会学衍生的数学

IF 3.2 2区社会学 Q1 SOCIOLOGY

Social Science Research Pub Date : 2025-02-01 DOI:10.1016/j.ssresearch.2024.103124

Burton H. Singer

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引用次数: 0

摘要

受劳动力流动性实证研究的启发，1970年，Sy Spilerman向我提出了一个问题，即在规定的时间内，通过Kolmogorov正反向微分方程，何时可以从单位矩阵I得到给定的随机矩阵P。1976年对时间齐次马尔可夫链的这个问题给出了一个完整的答案，从那以后，对时间非齐次的情况进行了研究，并在本文中进行了回顾。未来特别感兴趣的是马尔可夫链混合物的可达性/嵌入问题的解决方案。当观察到的马尔可夫链的过渡不满足可达性/嵌入条件时，未来也将研究马尔可夫链混合物的部分可识别性。

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On sociologically derived mathematics

Motivated by empirical studies of labor mobility, in 1970 Sy Spilerman approached me with a question about when a given stochastic matrix,

P

, can be reached from the identity matrix,

I

, in a prescribed period of time via the Kolmogorov forward and backward differential equations. A complete answer to this question for time-homogeneous Markov chains was provided in 1976—summarized herein—and a diversity of time-inhomogeneous cases have been studied since then and are reviewed in the present paper. Of particular interest for the future would be solutions for this reachability/embedding problem for mixtures of Markov chains. Also for the future would be studies of partial identifiability of mixtures of Markov chains when their observed transitions do not satisfy reachability/embedding conditions.

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来源期刊

Social Science Research SOCIOLOGY-

CiteScore

4.30

自引率

4.00%

发文量

审稿时长

65 days

期刊介绍： Social Science Research publishes papers devoted to quantitative social science research and methodology. The journal features articles that illustrate the use of quantitative methods in the empirical solution of substantive problems, and emphasizes those concerned with issues or methods that cut across traditional disciplinary lines. Special attention is given to methods that have been used by only one particular social science discipline, but that may have application to a broader range of areas.