Bayesian Methods for High-dimensional and Correlated Data

许多高通量生物技术的加速发展使得收集细胞中高维分子变化的测量数据变得负担得起，例如基因的表达，这些通常被称为特征，在生命科学文献中通常被称为签名。科学家们感兴趣的是发现与分类反应变量相关的特征，例如癌症的发病或进展。我们可以使用的候选特征的数量往往高达数百万。候选特征的高维度给统计学家带来了巨大的挑战，因为我们更有可能发现噪声而不是信号。此外，这些特征具有复杂的结构。我将致力于开发和应用基于MCMC(马尔可夫链蒙特卡罗)计算和重尾先验的贝叶斯统计方法，以确定与感兴趣的响应相关的特征子集，以及使用高通量数据的生命科学中的其他研究问题。这项研究的结果将包括用于解决生物信息学和神经信息学问题的新统计软件包(带有新算法)。预计这些软件包将促进新的科学发现，这将可能导致许多复杂人类疾病，特别是癌症的诊断和预后方面的进步。 我还建议扩展现有的模型评估方法，使其适用于相关数据的复杂贝叶斯模型，例如空间和时间数据，这些数据通常来自流行病学、生态和环境研究。我期望扩展的模型评估方法将成为评估相关数据模型的更可靠的工具。更好的模型评价结果不仅可以帮助我们选择最好的模型，还可以指导我们对现有模型进行改进，进而开发出更好的模型。因此，相关数据的扩展模型评估方法将有助于流行病学、生态和环境研究的研究人员为他们的数据集开发或选择合适的模型，然后根据他们的模型拟合结果得出可靠的结论并做出更好的预测。

The accelerated development of many high-throughput biotechnologies has made it affordable to collect measurements of high-dimensional molecular changes in cells, such as expressions of genes, which are called features generally, and often called signatures in the literature of life sciences. Scientists are interested in discovering relevant features associated with a categorical response variable, such as cancer onset or progression. The numbers of such candidate features at our disposal are often as large as millions. The high dimension in candidate features presents great challenges to statisticians because we are much more likely to find noise rather than signals. In addition, these features have complex structures. I will work to develop and apply Bayesian statistical methodologies based on MCMC (Markov chain Monte Carlo) computing and heavy-tailed priors to identify relevant feature subsets associated with a response of interest, and to other research problems in life sciences that use high-throughput data. The outcomes from this research will include new statistical software packages (with new algorithms) for solving bioinformatics and neuroinformatics problems. These software packages are expected to facilitate new scientific discoveries, which will potentially lead to advances in diagnosis and prognosis of many complex human diseases, particularly cancers. I also propose to extend existing model evaluation methods so that they are applicable to complex Bayesian models for correlated data, such as spatial and temporal data, which often arise from epidemiological, ecological, and environmental studies. I expect that the extended model evaluation methods will be more reliable tools for evaluating models for correlated data. Better model evaluation results will not only help us choose the best model, but also guide us to improve existing models and then develop better models. Therefore, the extended model evaluation methods for correlated data will assist investigators working in epidemiological, ecological, and environmental studies to develop or choose appropriate models for their data sets, and then draw reliable conclusions and make better predictions based on their model fitting results.