Nonparametric inference and Bayesian computing

我开发的非参数（在我以前的发现补助期间），到目前为止，在约束函数的推理背景下，已经证明工作得很好。这里所关注的函数基本上是受约束的，因为它们表征了copula，对于一个分布函数，具有均匀的边缘。Copula具有根本的重要性，因为它们保持了随机向量变量之间的整个依赖结构，因此它们在许多假设检验中自然出现。当它们与边缘相结合时，它们成为建模联合分布的强大工具。依赖结构的许多推理方法在许多应用科学中有具体的应用，如遗传学和计量经济学。推理方法通常是频率论的，在许多情况下是非参数的。在后一种情况下，与copula相关的过程（例如Kendall过程或经验copula过程）是主要的工作工具。这些通常不会导致有限样本的内在估计，并且经常需要修改它们以满足约束，这是一个不便之处。另一种方法是通过进一步利用问题的几何形状并提供无限维模型来构建模型，仍然保持易于处理。在这方面，我在未来几年有两个主要目标。

The nonparametrics that I developed (during the period of my previous discovery grant), so far in the context of inference on constrained functions, has shown to work well. The functions of interest here are constrained essentially because they characterize a copula, being for one a distribution function, with uniform margins. Copulas are of fundamental importance because they hold the entire dependency structure between the variates of a random vector, and so they appear naturally in many hypothesis tests. When they are combined with marginals, they become a powerful tool for modelling joint distributions. Much of the inferential methodology for the dependence structure has found concrete applications in many applied sciences, such as genetics and econometrics. The inferential approach is usually frequentist, and in many cases nonparametric. In the latter setup, processes linked to the copula (e.g the Kendall process, or empirical copula process) are the main working tools. These do not usually lead to intrinsic estimators for finite samples, and one often needs to modify them in order to satisfy the constraints, an inconvenience here. Another approach is to construct models by further exploiting the geometry of the problem and providing infinite dimensional models, still remaining tractable. Continuing in this direction, I have two main objectives for the next years.