Mathematical Sciences: Model Selection for Mixtures

题目：混合模型的选择摘要本文研究了当竞争模型涉及混合分布时选择合适模型的问题。提出了在指数分布的混合和卷积中选择模型的准则，并证明其渐近地接近于贝叶斯过程。将该准则的性能与基于复杂性的模型选择准则的性能进行了比较。然后将该方法应用于动物行为学的数据。使用越南生活水平调查的数据，还考虑了多元回归模型和逻辑回归模型混合的情况，并将其应用于越南的儿子偏好测试问题。在许多建模情况下，单个模型并不适合所有数据。例如，在调查越南等国家是否存在重男轻女（重男轻女）的显著统计证据时，由于一些家庭表现出重男轻女而另一些家庭没有表现出重男轻女的事实，问题变得更加复杂。行为学是行为科学的一个领域，关注对一个或多个个体的行为进行详细的观察和记录。在行为学中，关于一种行为是否可以分成连续的活动，还是几个活动的混合，出现了一些有趣的问题。这些问题可以通过统计混合建模来解决。

Proposal: DMS 9505196 PI: Dominique Haughton Institution: Bentley College Title: Model Selection for Mixtures Abstract This research is concerned with the problem of selecting a suitable model when the competing models involve mixtures of distributions. Criteria for model selection among mixtures and convolutions of exponential distributions are proposed and shown to be asymptotically close to Bayes procedures. The performance of the criteria are compared to that of complexity based model selection criteria. The methodology is then applied to data from ethological science. The case of mixtures of multiple regression models and logistic regression models is also considered and applied to the problem of testing for son preference in Vietnam, using data from the Vietnam Living Standard Survey. In many modeling situations, a single model is not suitable for all the data. For example, when investigating whether there is significant statistical evidence of son preference (preference for boys over girls) in countries such as Vietnam, the problem is complicated by the fact that some families display son preference and some do not. In ethological science, an area of behavioral science concerned with detailed observation and recording of the behavior of one or more individuals, interesting questions arise as to whether a behavior can be split into consecutive activities or is a mixture of several activities. These problems can be addressed by modeling with statistical mixtures.