Bayesian computational statistics

在我的博士论文中开发的贝叶斯非参数方法在copula估计的背景下表现得很好。虽然对联结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理时存在明显的缺点。本文的目标是得到固有估计量，以便对两者的不确定性提出连贯的处理，使用有限样本的分布估计和二元数据的预测。其思想是首先为联结函数构造非参数模型。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sup范数证明模型所张成的子空间是稠密的。选择参数集上的先验分布。参数空间的限制和后验分布的复杂性要求仔细选择MCMC技术进行推理。

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.