Nonparametric inference and Bayesian computing

到目前为止，我在关于受约束函数的推理的上下文中开发的非参数方法(在我之前的发现授权期间)已经被证明工作得很好。这里感兴趣的函数本质上是受限制的，因为它们的特征是Copula，其中一个是分布函数，具有一致的边距。联结具有基本的重要性，因为它们包含随机向量的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。当它们与边际相结合时，它们就成为模拟节理分布的强大工具。相依性结构的许多推理方法在许多应用科学中都有具体的应用，例如遗传学和计量经济学。推理方法通常是频繁的，在许多情况下是非参数的。在后一种设置中，与Copula相关联的过程(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本征估计，人们经常需要修改它们以满足约束，这在这里是不方便的。另一种方法是通过进一步利用问题的几何形状并提供仍然易于处理的无限维模型来构建模型。继续朝着这个方向前进，我对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.