Beyond Whittle's likelihood - new Bayesian semiparametric approaches to time series analysis

尽管非参数贝叶斯推理在过去十年中已经成为一个快速增长的话题，但只有很少的非参数贝叶斯方法被开发出来。主要的挑战在于需要指定一个似然函数的贝叶斯统计inference.Several作者解决了这个问题，使用惠特尔的似然近似贝叶斯建模的谱密度的平稳时间序列的主要非参数特征。即使对于非高斯平稳时间序列，这是不完全指定的第一和第二阶结构，惠特尔似然结果在许多情况下，渐近正确的统计推断，但往往在损失的效率为代价。另一方面，参数模型更强大，但如果模型指定错误，则会失败。时间序列的现代非参数自举方法面临类似的挑战，并隐式地使用真实似然的非参数或半参数近似。在这个项目中，我们将利用最先进的发展在引导领域的时间序列分析和联合收割机结合贝叶斯参数时间序列的似然在时域与频域校正的基础上非参数先验分布。这产生了一个全新的半参数方法贝叶斯时间序列分析。

Even though nonparametric Bayesian inference has been a rapidly growing topic over the last decade, only very few nonparametric Bayesian approaches to time series analysis have been developed. The main challenge lies in the necessity to specify a likelihood function for Bayesian statistical inference.Several authors solved this problem by using Whittle's likelihood as an approximation for Bayesian modeling of the spectral density as the main nonparametric characteristic of stationary time series. Even for non-Gaussian stationary time series, which are not completely specified by their first and second-order structure, the Whittle likelihood results in asymptotically correct statistical inference in many situations but often at the cost of a loss of efficiency. Parametric models, on the other hand, are more powerful but fail if the model is misspecified. Modern nonparametric bootstrap methods for time series face similar challenges and implicitly use non- or semiparametric approximations of the true likelihood. In this project, we will take advantage of state-of-the-art developments in the bootstrap realm of time series analysis and combine Bayesian parametric time series likelihoods in the time domain with a frequency-domain correction based on nonparametric prior distributions.This yields an entirely new semiparametric approach to Bayesian time series analysis.