Non-Gaussian latent variable mixture models

介绍

INTRODUCTION The applicant is proposing to develop novel latent variable mixture models, which can be used to jointly model mixed-type (binary, categorical, and continuous) data, and explore potential solutions to problems that are known to arise in the fitting of these types of models. Importantly, these solutions are likely to be applicable to a broad base of statistical models. For each aspect of the proposed research, it is the intention of the applicant to release free, open source, multi-platform software for fellow researchers and the public to access. OBJECTIVE The main objective of the proposed research is to push forward the methodology of latent variable mixture models, which will lead to a set of models with a wider range of applicability on real data sets. The current statistical models used are often based on the assumption of normally distributed data. Real world data does not always, or even commonly, conform to this assumption. Relaxing this assumption will lead to better insights for researchers across a variety of scientific fields and in industry. Students will play an integral role in the research of these methods, providing them with theoretical and practical training that will prepare them for future studies and employment opportunities. METHODS The focus of the proposed research is the mathematical development of the aforementioned models. This requires rigorous usage of calculus and linear algebra, under the chosen parameter estimation framework. The nature of the models being developed makes them computationally intensive; that is, they require an extremely large number of calculations. As such, the applicant makes heavy use of computers in his research, relying on algorithms to perform parameter estimation for the models he develops. These algorithms occasionally result in equations that cannot be solved directly. Part of the proposed research is to investigate alternate ways to approach these difficult equations. IMPACT The models alluded to in this summary are often used to classify groups that arise in data sets. As a concrete example of the importance of such methods, data is often obtained in medical fields on patients who have a particular disease and those who are healthy. The techniques introduced by the applicant may provide these researchers with an additional tool to determine `healthy' and `sick' groups within their data. Specifically, the proposed research would allow researchers to include categorical information (such as gender, ancestry, smoking habits, etc.) combined with numeric information (such as weight, height, blood cell counts, etc.) to aid in the estimation of whether a patient is likely to be `sick' or `healthy'.