捕获-再捕获模型的统计学原理

Statistical Principle for Capture-Recapture Model

捕获-再捕获模型由国外学者首创,最初用于野生动物总体规模估计,后来经过改进逐步应用于人口普查质量评估和其他统计领域。为了正确使用该模型,采取独一无二的方法,从试验背景、组格概率和边缘概率之间的关系、组格条件概率、条件多项分布和条件似然函数等方面对其进行全面解读和研究。研究表明:使用捕获-再捕获模型必须遵守三项理论原则:即总体封闭原则、个体同质原则、独立性原则;对实际问题与理论原则之间存在的差距必须做三件事情:即发现实际问题与理论原则之间的所有分歧点、评估各个分歧点问题的严重程度、寻找解决问题的办法。

Capture--recapture model was firstly developed by foreign scholars. It was originally used for wild animal population size estimation, later improved gradually and applied to census quality assessment and other statistical areas. This article undertakes comprehensive interpretation and research it from the experimental background, relationship between group lattice probability and edge probability, group lattice conditional probability, conditional multinomial distribution, conditional likelihood function, and so on by means of the one and only way in order to use the model correctly. Research shows that the use of capture--recapture models must adhere to the three theoretical principles, namely the overall closure principle, individual homogeneous principle and the principle of independence; three things must be done for the existing gap between the actual problems and theoretical principles, which includes to discover all bifurcation points between practical problems and theoretical principles, assess its severity for each bifurcation point, and find a solution to the problem.