一个集合理论框架枚举匹配的调查和它的应用，以减少不准确的车辆路边调查
A set theoretic framework for enumerating matches in surveys and its application to reducing inaccuracies in vehicle roadside surveys
摘要：
本文描述了一个框架，用于分析多个数据集的匹配。所描述的框架相当普遍，可适用于在若干地点（或在一个地点若干天）调查的数据中发现匹配的各种问题。作为一个例子，该框架被应用到车牌调查数据中的错误匹配问题。所解决的具体问题是，当由于所进行的调查的性质而有可能意外地混淆两辆车时，估计在多个调查点中的每一个调查点有多少辆车是真正被看到的。在本文中，一种方法，用于表示可能的“类型的匹配”的概述使用集合论。本文将对“匹配类型”进行定义和形式化。描述了一种在n个调查点上枚举所有匹配类型的集合的方法。该方法适用于使用一个简单的probabalistic方法的错误匹配的校正调查数据的问题。一种算法的开发，用于纠正多个调查站点的错误匹配，并证明其使用与模拟结果。
英文摘要：
This paper describes a framework for analysing matches in multiple data sets. The framework described is quite general and can be applied to a variety of problems where matches are to be found in data surveyed at a number of locations (or at a single location over a number of days). As an example, the framework is applied to the problem of false matches in licence plate survey data. The specific problem addressed is that of estimating how many vehicles were genuinely sighted at every one of a number of survey points when there is a possibility of accidentally confusing two vehicles due to the nature of the survey undertaken. In this paper, a method for representing the possible "types of match" is outlined using set theory. The phrase "types of match" will be defined and formalised in this paper. A method for enumerating the set of all types of match over n survey sites, is described. The method is applied to the problem of correcting survey data for false matches using a simple probabalistic method. An algorithm is developed for correcting false matches over multiple survey sites and its use is demonstrated with simulation results.
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