Mathematical Sciences: Statistical Theory for Classification

概率模型可以用来区分自然发生的观察群，即使这些观察是混合的和未标记的。已建立的理论借鉴了混合模型、模态模型以及进化分类的广义马尔可夫模型。本文介绍并研究了一类新的概率模型：积划分模型。这将在确定分类和基于部分或完全分类的预测中有广泛的应用。这些分类算法的应用包括构建进化树、识别建模过程的变化点、图像重建以及对航天飞机等复杂情况的故障预测。

Probability models can be used to distinguish naturally occurring clusters of observations even when these observations are intermixed and unlabelled. Established theory draws on mixture models, modal models, and, for evolutionary classification, generalized Markov models. This research introduces and investigates a new class of probability models: product partition models. These will have wide application in determining classifications and in predicting based on partial or complete classifications. Applications for these classification algorithms include the construction of evolutionary trees, recognition of change-points for modelled processes, image reconstruction, and failure prediction for complex cases like the space shuttle.