Mathematical Sciences: Model Selection for Mixtures

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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.