Bayesian computational statistics

在我的博士论文中开发的贝叶斯非参数方法已经证明在Copula估计的背景下工作得很好。虽然Copula函数的频率估计通常具有良好的渐近性质，但其中一些估计在使用有限样本进行推断时存在显著的缺陷。本文的目标是得到内在估计量，以便对有限样本分布估计和双变量数据预测的不确定性提出一致的处理方法。其思想是首先构造Copula函数的非参数模型。这里的非参数性质意味着模型中的参数数量可以任意大。然后根据超范数证明了该模型所跨越的子空间在Copula空间中是稠密的。选择参数集合上的先验分布。对于参数空间的约束和由此产生的后验分布的复杂性，需要仔细选择MCMC技术来进行推理。

The Bayesian nonparametric methodology developed in my Ph.D thesis has shown to work well in the context of copula estimation. Although frequentist estimators for the copula function usually have good asymptotic properties, some of them present notable drawbacks for inference using finite samples. The goal of the thesis is to get intrinsic estimators in order to propose a coherent treatment of the uncertainty relative to both, the estimation of the distribution using a finite sample and to the prevision of bivariate data. The idea is first to construct a nonparametric model for the copula functions. The nonparametric nature here means that the number of parameters in the model can be made arbitrarily large. The subspace spanned by the model is then shown to be dense in the space of copulas according to the sup norm. A prior distribution over the set of parameters is selected. The constraints on the parameter space and the complexity of the resulting posterior distribution requires carefully chosen MCMC techniques for inference.