Nonparametric Bayesian Regression for Categorical Responses: Novel Methodology for Modeling, Inference and Applications

研究者开发了灵活的贝叶斯混合模型和相应的方法，用于推断一些有序分类响应的回归问题。更具体地说，开发的方法：二元响应的非参数混合回归;有序回归，包括多变量有序响应和混合有序连续响应;有序回归关系的动态建模;以及有序分类的生物测定剂量-响应研究的建模和风险评估。所有的方法都建立在非参数先验的基础上，包括一般的混合先验模型以及由模型的应用领域和推理目标所激发的更结构化的形式。主要研究活动涉及灵活的回归建模，其基于由协变量值索引的响应分布过程的非参数先验或响应和协变量的联合分布的非参数混合模型。这些类别的模型能够为回归关系和条件响应分布提供丰富的推断。因此，与标准参数模型相比，它们提高了模型拟合和预测性能，而且相对于现有的贝叶斯半参数工作也是如此。对于所有正在开发的建模方法，研究者研究相关的理论特性，模型规范，先验启发，马尔可夫链蒙特卡洛后验模拟技术，以及模型检查和比较。有序分类响应的回归问题-涉及有序尺度上记录的响应变量和相关解释变量的数据-在生物医学的各个领域都具有关键重要性，环境和社会科学。随着这些领域的研究人员收集越来越多的涉及有序反应的数据，特别是随着时间或时间和空间的推移，需要进行分析，以增强他们对潜在过程的理解。这激发了对足够丰富的统计模型的需求，这些模型可以容纳一般的有序回归关系。这项研究的主要动机是扩大有序回归建模工具的目录提供给这样的科学家，在这个过程中扩大的方法在贝叶斯nonparametrics领域，贝叶斯统计的一个新兴领域。由于其通用性，在这个研究项目下开发的统计方法有可能在几个科学领域的实质性应用。一个特别有前途的应用领域涉及进化生物学问题的自然选择的形式估计，因为它涉及表型性状的有序健身措施，如生存，成熟或繁殖成功。对于这样的设置，改进估计的健身表面，以及了解其时间和/或空间的演变可以有一个有效的决策所研究的人口的影响。

The investigator develops flexible Bayesian mixture models and corresponding methods for inference for a number of regression problems with ordinal categorical responses. More specifically, methodology is developed for: nonparametric mixture regression for binary responses; ordinal regression, including multivariate ordinal responses and mixed ordinal-continuous responses; dynamic modeling for ordinal regression relationships; and modeling and risk assessment for bioassay dose-response studies with an ordinal classification. All the methods build from nonparametric priors, including both general mixture prior models as well as more structured forms as motivated by the application area and inferential objectives of the model. The key research activity involves flexible regression modeling based on either dependent nonparametric priors for the process of response distributions indexed by covariate values or nonparametric mixture models for the joint distribution of the response(s) and covariates. These classes of models enable rich inference for both the regression relationship and for the conditional response distribution. Hence, they improve model fit and predictive performance compared to standard parametric models, but also relative to existing Bayesian semiparametric work. For all the modeling approaches under development, the investigator studies relevant theoretical properties, model specification, prior elicitation, Markov chain MonteCarlo posterior simulation techniques, and model checking and comparison.Regression problems with ordinal categorical responses -- involving data on response variables recorded on an ordinal scale and on associated explanatory variables -- are of key importance in various fields of the biomedical, environmental and social sciences. As researchers from these fields collect more and more data involving ordinal responses, especially over time or time and space, the need for analyses that enhance theirunderstanding of underlying processes grows. This inspires the need for sufficiently rich statistical models that can accommodate general ordinal regression relationships. The primary motivation for this research is to expand the catalog of ordinal regression modeling tools available to such scientists, in the process expanding the methodology in the field of Bayesian nonparametrics, a burgeoning area of Bayesian statistics. Due to their generality, the statistical methods developed under this research project have the potential for substantive applications in several scientific fields. A particularly promising area of application involves evolutionary biology problems on estimation of the form of natural selection as it relates phenotypic traits to ordinal fitness measures, such as survival, maturity or reproductive success. For such settings, improved estimation of the fitness surface as well as understanding of its temporal and/or spatial evolution can have an impact on effective decision making for the population under study.