论文标题
非参数贝叶斯预测非均匀泊松过程的收缩先验
Shrinkage priors for nonparametric Bayesian prediction of nonhomogeneous Poisson processes
论文作者
论文摘要
我们考虑了具有未知强度功能的非均匀泊松过程模型的非参数贝叶斯估计和预测。我们为强度功能提出了一类不正确的先验。基于类不当的先验，非参数贝叶斯与核混合物的推断被证明是有用的，尽管不正确的先验尚未被广泛用于非参数贝叶斯问题。与有限维独立泊松模型相对应的几种定理适用于具有无限维参数空间的非均匀泊松过程模型。根据kullback-leibler损失，基于不当先验的贝叶斯估计和预测被证明是可以接受的。研究了基于先验的贝叶斯推断的数值方法。
We consider nonparametric Bayesian estimation and prediction for nonhomogeneous Poisson process models with unknown intensity functions. We propose a class of improper priors for intensity functions. Nonparametric Bayesian inference with kernel mixture based on the class improper priors is shown to be useful, although improper priors have not been widely used for nonparametric Bayes problems. Several theorems corresponding to those for finite-dimensional independent Poisson models hold for nonhomogeneous Poisson process models with infinite-dimensional parameter spaces. Bayesian estimation and prediction based on the improper priors are shown to be admissible under the Kullback--Leibler loss. Numerical methods for Bayesian inference based on the priors are investigated.
