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.

翻译：我们认为非参数性贝叶斯估计和预测具有未知强度功能的非对等性波斯森进程模型。我们建议对强度功能有一类不适当的前科。根据等级不适当的前科,对内核混合物的非对等贝斯人推断和预测是有用的,虽然对非参数性贝斯人问题没有广泛使用不适当的前科。对具有无限参数空间的非对等性波斯森进程模型中与有限维度独立波斯森模型中相对应的一些理论。在Kullback-Leiberr损失中,根据不适当的前科进行的巴伊西亚人估计和预测被证明是可以接受的。对基于前科的巴伊斯人推断的数值方法进行了调查。