Non-Gaussian latent variable mixture models

介绍*申请人建议开发新的潜变量混合模型，该模型可用于对混合类型(二进制、分类和连续)数据进行联合建模，并探索在拟合这些类型的模型时出现的已知问题的潜在解决方案。重要的是，这些解决方案可能适用于广泛的统计模型。对于拟议研究的每一个方面，申请者的意图是发布免费、开源、多平台的软件，供同行和公众访问。**目标*拟议研究的主要目标是推动潜变量混合模型的方法学，这将导致一套在真实数据集上具有更广泛适用性的模型。目前使用的统计模型往往是基于正态分布数据的假设。现实世界的数据并不总是、甚至通常不符合这一假设。放松这一假设将为各个科学领域和行业的研究人员带来更好的洞察力。学生将在这些方法的研究中发挥不可或缺的作用，为他们提供理论和实践培训，为他们未来的学习和就业机会做好准备。**方法*建议研究的重点是上述模型的数学发展。这需要在选定的参数估计框架下严格使用微积分和线性代数。正在开发的模型的性质使得它们需要大量的计算；也就是说，它们需要非常大量的计算。因此，申请人在他的研究中大量使用计算机，依靠算法对他开发的模型进行参数估计。这些算法有时会导致无法直接求解的方程。拟议的研究的一部分是探索处理这些困难方程的替代方法。**影响*本摘要中提到的模型通常用于对数据集中出现的组进行分类。作为这种方法重要性的一个具体例子，通常在医学领域获得关于患有特定疾病的患者和健康的患者的数据。申请人介绍的技术可为这些研究人员提供另一种工具，以确定其数据中的“健康”和“患病”群体。具体地说，拟议的研究将允许研究人员包括分类信息(如性别、血统、吸烟习惯等)。结合数字信息(如体重、身高、血细胞计数等)以帮助估计病人可能是“生病的”还是“健康的”。

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'.