Mathematical Sciences: Model Selection for Mixtures

建议：DMS 9505196 PI：Dominique Haughton Institution：Bentley College标题：混合模型选择摘要本研究关注的是当竞争模型涉及分布的混合模型时选择合适的模型的问题。提出了指数分布的混合模型和卷积模型的选择准则，并证明了其渐近于贝叶斯过程。与基于复杂度的模型选择准则的性能进行了比较。然后，这种方法被应用于来自行为学的数据。多元回归模型和Logistic回归模型的混合情况也被考虑并应用于越南的男孩偏好测试问题，使用的数据来自越南生活水平调查。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男孩偏好(重男轻女)的显著统计证据时，一些家庭表现出男孩偏好，而另一些家庭则没有，这一事实使问题复杂化。在行为学中，行为科学的一个领域，涉及对一个或多个个体的行为的详细观察和记录，出现了一些有趣的问题，即一个行为是否可以分为连续的活动，或者是几个活动的混合。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.